(a) [tex]P(|X^2 - Y| < 5)[/tex] = 0.02 + 0.06 + 0.20 + 0.23 = 0.51. (b) The marginal mass function of X is: P(X = -2) = 0.20, P(X = 1) = 0.30, P(X = 3) = 0.50.
(c) E([tex]X^2 - Y[/tex]) = ΣxΣy ([tex]x^2 - y[/tex]) P(X = x, Y = y). (d) X & Y are independent.
(a) To compute [tex]P(|X^2 - Y| < 5)[/tex] we need to find the probability of all the joint mass function values for which the absolute difference between [tex]X^2[/tex] and Y is less than 5.
[tex]P(|X^2 - Y| < 5) [/tex][tex]= P((X^2 - Y) < 5) - P((X^2 - Y) < -5)[/tex]
= [tex]P(X^2 - Y = -2) + P(X^2 - Y = 1) + P(X^2 - Y = 3) + P(X^2 - Y = 0)[/tex]
From the table, we can see that:
[tex]P(X^2 - Y = -2) = 0.02[/tex]
[tex]P(X^2 - Y = 1) = 0.06[/tex]
[tex]P(X^2 - Y = 3) = 0.20[/tex]
[tex]P(X^2 - Y = 0) = P(X^2 = Y)[/tex]
= 0.04 + 0.09 + 0.10 = 0.23
[tex]P(|X^2 - Y| < 5)[/tex] = 0.02 + 0.06 + 0.20 + 0.23 = 0.51
(b) To find the marginal mass function of X,
we sum the joint mass function values for each value of X.
P(X = -2) = 0.02 + 0.04 + 0.06 + 0.08 = 0.20
P(X = 1) = 0.03 + 0.06 + 0.09 + 0.12 = 0.30
P(X = 3) = 0.05 + 0.10 + 0.15 + 0.20 = 0.50
(c) To compute [tex]Var(X^2 - Y)[/tex]
we first calculate [tex]E(X^2 - Y)[/tex] and
[tex]E((X^2 - Y)^2)[/tex][tex]=E(X^2 - Y)[/tex]
= ΣxΣy [tex](x^2 - y)[/tex]
P(X = x, Y = y)
[tex]= (-2)^2(0.02) + (-2)^2(0.04) + (-2)^2(0.06) + (-2)^2(0.08) + 1^2(0.03) + 1^2(0.06) + 1^2(0.09) + 1^2(0.12) + 3^2(0.05) + 3^2(0.10) + 3^2(0.15) + 3^2(0.20)[/tex]
= 1.13
[tex]E((X^2 - Y)^2) [/tex] = ΣxΣy [tex](x^2 - y)^2[/tex]
P(X = x, Y = y)[tex]= (-2)^4(0.02) + (-2)^4(0.04) + (-2)^4(0.06) + (-2)^4(0.08) + 1^4(0.03) + 1^4(0.06) + 1^4(0.09) + 1^4(0.12) + 3^4(0.05) + 3^4(0.10) + 3^4(0.15) +[/tex]
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When describing the results of an observational study, the mathematical relationship between the relative risk (RR) and the odds ratio (OR) is referred to as: a. The rare disease assumption b. The built-in bias c. The relative odds approach d. Effect modification e. All of the above
Previous question
The mathematical relationship between the relative risk (RR) and the odds ratio (OR) is (c) The relative odds approach.
How to find the mathematical relationship between the relative risk (RR) and the odds ratio (OR)?The mathematical relationship between the relative risk (RR) and the odds ratio (OR) is often described as the relative odds approach.
This approach quantifies the relationship between RR and OR and provides insights into the association between exposure and outcome in observational studies.
The rare disease assumption (a) refers to the assumption made in case-control studies that the odds ratio approximates the relative risk when the outcome is rare.
It is not specifically related to the mathematical relationship between RR and OR.
The built-in bias (b) does not directly relate to the mathematical relationship between RR and OR.
It refers to biases inherent in the study design or data collection process.
Effect modification (d) refers to a situation where the association between an exposure and outcome differs depending on the levels of another variable.
While effect modification can influence the relationship between RR and OR, it is not the specific term used to describe their mathematical relationship.
In summary, the mathematical relationship between RR and OR is best described as the relative odds approach (c), while the other options (a, b, d) are not directly related to this specific relationship.
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Saul's Corner Market sells large candy bars for $2 each. A bag of pretzels is $3. On Tuesday, the store sold twice
as many candy bars as Monday but the same number of pretzels. On Wednesday, the store sold the same
number of candy bars as Monday but only half the amount of pretzels. On Thursday, the store sold three times
as much as they sold on Tuesday. On Friday, the store sold 12 fewer candy bars and 5 more bags of pretzels
compared to Wednesday.
Let c represent the number of candy bars sold and p represent the number of pretzels sold on Monday. Write
an expression for each day to show the amount of money that the store brought in from candy bars and
pretzels.
1. Monday
2. Tuesday
3. Wednesday
4. Thursday
5. Friday
6. Monday through Friday
Answer:
Step-by-step explanation:
Monday: c and p
Tuesday: 2c+p
Wednesday: 2c+p/2
Thursday: 6c+3p/2
Friday: (2c-12)+(p/2+5)
Adding them all up, you get, for Monday-Friday: (13c-12)+(9p/2+5)
I'm not sure how to explain this to you though, you just follow the directions they gave, to multiply and subtract.
Hope this is helpful!
Find the values of the sine, cosine, and tangent for angle a
[tex]sina=\frac{2\sqrt{13} }{13} \\cosa=\frac{3\sqrt{13} }{13}\\tana=\frac{2}{3}[/tex]
Answer:
A.
Step-by-step explanation:
correct on edge2021
If p is prime, then there exists a field of order p². O True False
The statement "If p is prime, then there exists a field of order p²" is true. For any prime number p, there exists a finite field of order p².
Is it true that if p is prime, there exists a field of order p²?Yes, it is true that if p is a prime number, then there exists a field of order p². In mathematics, a field is a specific type of algebraic structure with two operations, addition and multiplication, that satisfy certain properties. The order of a field refers to the number of elements in the field. For any prime number p, there exists a unique finite field of order p², often denoted as GF(p²) or Fp². This field consists of p² elements and is crucial in various areas of mathematics, such as number theory, cryptography, and coding theory.
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Andrea and Tim are picking apples. Andrea picks 4 à pounds of apples. Tim picks
33 pounds of apples. How many total pounds of apples did Andrea and Tim
pick?
Answer:
37 pounds of apples.
Step-by-step explanation:
you add together the amount of apples that both people have gathered, which in this case would be 33+4 which makes 37, so your answer would be 37 apples.
Given some scores on an entrance exam, which are roughly normally distributed, we are told they have a mean of 82 and a standard deviation (std dev) of 5. If some student received a 90 on the exam, what would there z-score be calculated as?
The z-score for a student who received a score of 90 on the entrance exam is 1.6.
What is the formula for calculating the area of a triangle?The z-score for a student who received a score of 90 on the entrance exam, with a mean of 82 and a standard deviation of 5, can be calculated as follows:
z = (x - μ) / σx is the student's score (90 in this case)μ is the mean (82)σ is the standard deviation (5)Plugging in the values:
z = (90 - 82) / 5Simplifying:
z = 8 / 5Calculating:
z = 1.6Therefore, the z-score for the student who received a score of 90 on the exam is 1.6.
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Ared candle is 8 inches tall and burns at a rate of inch per hour. 1 A blue candle is 6 inches tall and burns at a rate of inch per hour. 5 After how many hours will both candles be the same height? Enter your answer in the box.
Answer:
After 8 hrs both candles would've burned out completely, so they'll, more or less, be at the same height.
Help is much needed. You will get lots of point too!
Which is closest to the height of a pine tree?
1. 9 inches
2. 9 Yards
3. 9 Miles
Answer:
2/b
Step-by-step explanation:
9 yards
Help please
Mark True or False in the table on your answer document to indicate whether
each comparison is true
Answer:
1. false
2. false
3. true
Step-by-step explanation:
Find the value of each trigonometric ratio. Express your answer as a fraction in lowest terms .
Answer:
The answers are in the attachment above
good day mate
Angle ∠B is a right-angle then the measure of angle ∠A is 43.6 degrees and the measure of angle ∠C is 46.4 degrees.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.
The triangle ΔABC is given.
The angle ∠B is a 90°.
Then the value of the angle ∠C will be
[tex]\rm C = \sin ^{-1} \dfrac{21}{29}\\\\C = 46.40^o[/tex]
Then the value of the angle ∠A will be
∠A + ∠C = 90°
∠A + 46.40° = 90°
∠A = 43.6°
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Suppose you toss a coin and will win $1 if it comes up heads. If it comes up tails, you toss again. This time you will receive $2 if it comes up heads. If it comes up tails, toss again. This time you will receive $4 if it is heads. Continue in this fashion for a total of 10 flips of the coin, after which you receive nothing if it comes up tails. What is the mathematical expectation for this game?
Answer:
5
Step-by-step explanation:
The winnings are in G.P. : 1, 2, 4, ..... till 10 toss.
[tex]$a_n = 1 \times 2^{n-1}\ \ \ \forall \ n = 1,2,3,4,....,10$[/tex]
[tex]$a_n$[/tex] denotes the winnings on the [tex]$n^{th}$[/tex] toss.
The probability of earning amount [tex]$a_n$[/tex] on the [tex]$n^{th}$[/tex] toss is = [tex]$\left(\frac{1}{2}\right)^n$[/tex]
∴ [tex]$E(X) = \sum_{n=1}^{10} \ a_n \times \left(\frac{1}{2}\right)^n $[/tex]
[tex]$=\sum_{n=1}^{10} \ 1 \times \frac{2^{n-1}}{2^n} $[/tex]
[tex]$=\sum_{n=1}^{10} \ \frac{1}{2}$[/tex]
Sum of the 1st n terms of the A.P. is :
[tex]$=\frac{n}{2}[2a+(n-1)d] $[/tex]
[tex]$=\frac{10}{2}[2\times \frac{1}{2}+(10-1)\times 0] $[/tex]
= 5
Therefore, E(X) = 5
Hence the expected value of the game is 5
PLSSS HELP IMMEDIATELY!!!! i’ll give brainiest, if u don’t provide just a link! answer choices: (4,6) , (0,1) , (0,0) , (5,4)
Answer:
try (4,5)
Step-by-step explanation:
that is where the points meet I think it is that I am not sure sorry if it is wrong
Please help me with the question please ASAP ASAP please please ASAP please please help
* It’s NOT 24 if you get 24
Answer:
The tree is 8 foot long
hope this helps
good day mate
Answer:
8
Step-by-step explanation:
12:6 = x:4
2:1 = x:4
x=8
A school janitor has mopped 1/3 of a classroom in 5 minutes. At what rate is he mopping?
simplify your answer and write it as a proper fraction, mixed number, or whole numer.
___ classrooms per minute
Given,A school janitor has mopped 1/3 of a classroom in 5 minutes.We have to find the rate at which he is mopping.Using the concept of unitary method,Rate of mopping 1 classroom in 5 × 3 = 15 minutes= 1/15 of a classroom in 1 minute.Rate of mopping 1/3 classroom in 5 minutes = (1/3) ÷ 5= 1/15 classroom per minuteHence, the required rate at which he is mopping is 1/15 classroom per minute.
Answer: 1/15.
To determine the rate at which the janitor is mopping, we can calculate the fraction of the classroom mopped per minute.
Given that the janitor mopped 1/3 of the classroom in 5 minutes, we can express this as:
(1/3) classroom / 5 minutes
To simplify this fraction, we divide the numerator and denominator by the greatest common divisor, which is 1:
(1/3) classroom / (5/1) minutes = (1/3) classroom × (1/5) minutes
Multiplying the numerators and the denominators gives us:
1 classroom × 1 minute / 3 × 5
Simplifying further:
1 classroom × 1 minute / 15
Therefore, the rate at which the janitor is mopping is 1/15 classrooms per minute.
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The given information is that the janitor mopped 1/3 of a classroom in 5 minutes. We have to find out at what rate is he mopping.
The rate of mopping is 1/15 classrooms per minute.
Let's try to solve the problem below. The given fraction is 1/3 of a classroom that was mopped in 5 minutes. We need to find the rate of mopping which can be calculated by dividing the fraction of the classroom mopped by the time it took to mop it. The rate of mopping can be found by performing the following calculation:
Rate of mopping = Fraction of the classroom mopped/Time taken to mop
= 1/3/5
= 1/15
So the rate of mopping is 1/15 classrooms per minute. This is the simplified answer.
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AC and BD are diameters of the given circle. OC is 6 centimeters and ABO = CBO. what is AO. A 3/ B 4/ C 5/ D 6
Answer:
A
Step-by-step explanation:
The following data are cost (in cents) per ounce for nine different brands of sliced Swiss cheese (www .consumerreports.org):
29 62 37 41 70 82 47 52 49
a. Compute the variance and standard deviation for this data set. s2 = 279.111; s = 16.707
b. If a very expensive cheese with a cost per slice of 150 cents was added to the data set, how would the values of the mean and standard deviation change?
a. The variance of the data set is 279.111 and the standard deviation is 16.707.
b. Adding an expensive cheese increases the mean to 55.9 and the standard deviation to 48.53.
a. To compute the variance and standard deviation for the given data set, we can use the following formulas:
Variance (s²) = [(Σx²) - (Σx)² / n] - 1
Standard Deviation (s) = √(Variance)
Using the given data set: 29, 62, 37, 41, 70, 82, 47, 52, 49
Step 1: Calculate the mean (x) of the data set.
Mean (x) = (Σx) / n
Σx = 29 + 62 + 37 + 41 + 70 + 82 + 47 + 52 + 49 = 409
n = 9 (number of data points)
Mean (x) = 409 / 9 = 45.44 (rounded to two decimal places)
Step 2: Calculate the sum of squares (Σx²) for the data set.
Σx² = 29² + 62² + 37² + 41² + 70² + 82² + 47² + 52² + 49² = 151509
Step 3: Substitute the values into the variance formula and calculate the variance.
Variance (s²) = [(Σx²) - (Σx)² / n] - 1
Variance (s²) = (151509 - (409)² / 9) / (9 - 1) = 279.111 (rounded to three decimal places)
Step 4: Calculate the standard deviation by taking the square root of the variance.
Standard Deviation (s) = √(Variance)
Standard Deviation (s) = √279.111 = 16.707 (rounded to three decimal places)
b. If a very expensive cheese with a cost per slice of 150 cents was added to the data set, the values of the mean and standard deviation would change. To find the new mean and standard deviation, we need to incorporate the additional data point and recalculate.
New Σx = Σx + 150 = 409 + 150 = 559 (updated sum of the data points)
New n = n + 1 = 9 + 1 = 10 (updated number of data points)
New Mean (x) = New Σx / New n = 559 / 10 = 55.9 (rounded to one decimal place)
The addition of the expensive cheese increased the mean.
To calculate the new variance and standard deviation, we follow the same steps as in part a using the updated Σx and n values:
New Σx² = Σx² + (150)² = 151509 + 22500 = 174009
New Variance (s²) = [(New Σx²) - (New Σx)² / New n] - 1 = (174009 - (559)² / 10) / (10 - 1) = 2355 (rounded to three decimal places)
New Standard Deviation (s) = √New Variance = √2355 = 48.53 (rounded to two decimal places)
Therefore, the addition of the expensive cheese increased both the mean and the standard deviation of the data set.
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Write 9020000 in standard form?
Answer:
9.02 x 10^6
Step-by-step explanation:
hope this helps!
Find the indicated critical z value. Find the value of z a/2 that corresponds to a confidence level of 85%. a/2 Answer:
The critical z value for a confidence level of 85% is approximately 1.44.
To understand this better, let's delve into the concept of confidence level. A confidence level is a measure of the uncertainty or margin of error associated with an estimation. In this case, we are given a confidence level of 85%, which means that we want to be 85% confident that the true population parameter falls within a specific range.
To find the critical z value, we need to determine the z value that leaves a certain percentage in the tails of the standard normal distribution. Since the confidence level is 85%, we divide this value by 2 to get a/2, which is 0.85/2 = 0.425. This value corresponds to the area under the curve in one tail of the distribution.
Using a standard normal distribution table or a statistical software, we can find the z value that corresponds to a cumulative probability of 0.425. The closest z value to this probability is approximately 1.44. Therefore, the critical z value for a confidence level of 85% is approximately 1.44.
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Question is in picture
Answer:
27.5ft
Step-by-step explanation:
a² + b² = c²
Plug in what you have:
a² + 12² = 30²
Get a by itself:
a² = 30² - 12²
Simplify:
a² = 900 - 144
Simplify:
a² = 756
Simplify:
√a = √756
Then you get 27.49 and when you round you get 27.5
The high school soccer team can have no more
than 22 players on the roster. Write and solve an
inequality finding the number of players the
coach may choose if the coach already has 13
players.
Answer:
13 + x ≤ 22
x ≤ 9
Step-by-step explanation:
Total players = 22
Players available = 13
Players remaining = x
The inequality can be written as:
Players available + Players remaining ≤ Total players
13 + x ≤ 22
x ≤ 22 - 13
x ≤ 9
Graph each set of numbers on the number line and order the numbers from greatest to least 0.5, -1, -1/4, 0
Answer:
0.5, 0, -1/4, -1
The Σx = 68, y = 79, xy = 1200 x² = 600 and N = 12 determine the equation of the least square line. Leave answer in 2 decimal places.
To determine the equation of the least squares line, we need to find the slope (m) and the y-intercept (b) using the given data. The formula for the least squares line is:
y = mx + b
where:
m is the slope of the line
b is the y-intercept of the line
We can use the following formulas to calculate the slope and y-intercept:
m = (NΣxy - ΣxΣy) / (NΣx² - (Σx)²)
b = (Σy - mΣx) / N
Given the values:
Σx = 68
Σy = 79
Σxy = 1200
Σx² = 600
N = 12
Let's substitute these values into the formulas:
m = (12 * 1200 - 68 * 79) / (12 * 600 - (68)²)
b = (79 - m * 68) / 12
Calculating the values:
m = (14400 - 5372) / (7200 - 4624)
m = 9028 / 2576
m ≈ 3.5039
b = (79 - 3.5039 * 68) / 12
b = (79 - 238.2752) / 12
b ≈ -13.2738
Therefore, the equation of the least squares line is:
y ≈ 3.5039x - 13.2738
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The equation of the least squares line is y = 1.25x + 10.75
To determine the equation of the least squares line, we need to find the slope (b) and y-intercept (a) using the following formulas:
b = (NΣxy - ΣxΣy) / (NΣx² - (Σx)²)
a = (Σy - bΣx) / N
Given the following values:
Σx = 68
Σy = 79
Σxy = 1200
Σx² = 600
N = 12
Let's calculate the slope (b) first:
b = (12 × 1200 - 68×79) / (12×600 - 68²)
b ≈ 1.25
Now we can calculate the y-intercept (a):
a = (79 - 1.25×68) / 12
a = 10.75
Therefore, the equation of the least squares line is: y = 1.25x + 10.75.
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Use pie= 22/7 to approximate the circumference of a circle whose diameter is 28 inches.
Answer:
88 inches
Step-by-step explanation:
formula for circumference: 2pir or pi*diameter
22/7*28=88
88 inches
Need help solving this problem.
Answer:
The measure of angle CDE is 37 degrees
Step-by-step explanation:
A soccer ball has an interior
diameter of 22cm. How
many cubic centimeters of air
does a soccer ball contain,
rounded to the nearest
hundredth?
Answer:
5575 cm³
Step-by-step explanation:
The volume of a sphere is V = (4/3)πr³. If we substitute r = (d/2 where r is the radius and d the diameter), this formula becomes:
πd³
V = (4/3)π·d³/8, or V = -------------
6
and so, if d = 22 cm, the volume is:
π(22 cm)³
V = ------------------- = 5575 cm³
6
PLZZZZZ HELP ASAP!
Jake has $5,625 in his savings account. Each month he makes a car payment from his savings account without making additional deposits.
Which table shows the amount of money in Jake's savings account after each month if it is a linear relationship?
Please help me it’s due today
HELP WILL MARK BRAINLIEST
Answer:
The answer is a...............
A survey of 150 college students was done to find out what elective course they were taking Lot A the set of those taking ort, B the set of those taking basketweaving, and C - the set of those taking canoeing. The study revealed the following information A-45 IAN B = 12 181 55 ANC-15 C-40 BC-2 Anno 2 How many students were not taking any of these electives?
A survey of 150 college students was done to find out what elective course they were taking Lot A the set of those taking ort, B the set of those taking basketweaving, and C - the set of those taking canoeing. The study revealed the following information A-45 IAN B = 12 181 55 ANC-15 C-40 BC-2 Anno 2
Based on the given information, we can calculate the number of students who were not taking any of the elective courses.
Let's break down the information provided:
A: The set of students taking Art elective = 45
B: The set of students taking Basket weaving elective = 12
C: The set of students taking Canoeing elective = 40
A ∩ B: The set of students taking both Art and Basket weaving electives = 2
A ∩ C: The set of students taking both Art and Canoeing electives = 15
B ∩ C: The set of students taking both Basket weaving and Canoeing electives = 0 (not specified)
A ∩ B ∩ C: The set of students taking all three electives = 2
To find the number of students who were not taking any of these electives, we need to subtract the total number of students taking at least one elective from the total number of students surveyed.
Total students surveyed = 150
Students taking at least one elective = A ∪ B ∪ C
Students taking at least one elective = A + B + C - (A ∩ B) - (A ∩ C) - (B ∩ C) + (A ∩ B ∩ C)
Students taking at least one elective = 45 + 12 + 40 - 2 - 15 - 0 + 2
Students taking at least one elective = 82
Students not taking any of these electives = Total students surveyed - Students taking at least one elective
Students not taking any of these electives = 150 - 82
Students not taking any of these electives = 68
Therefore, there were 68 students who were not taking any of the elective courses using set theory.
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