The joint probability mass function of X and Y is given by p(1, 1) = 0.4 p(1,2) = 0.1 p(1,3) = 0.05 p(2, 1) = 0.05 p(2, 2) = 0.05 p(2, 3) = 0.05 p(3, 1) = 0.1 p(3, 2) = 0.1 p(3, 3) = 0.1 (a) Compute the conditional mass function of Y given X = 3: P(Y = 1|X = 3) = %3D P(Y = 2|X = 3) = %3D P(Y = 3|X = 3) = (b) Are X and Y independent? (enter YES or NO) (c) Compute the following probabilities: P(X+Y > 2) = %3D P(XY = 2) = P(주 > 1) =

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The joint probability mass function of X and Y is given by
p(1, 1) = 0.4
p(1, 2) = 0.1
p(1,3) = 0.05
p(2, 1) = 0.05 p(2, 2) = 0.05 p(2,3) = 0.05
p(3, 2) = 0.1
p(3, 1) = 0.1
p(3,3) = 0.1
(a) Compute the conditional mass function of Y given X = 3: P(Y = 1|X = 3) =
P(Y = 2|X = 3) =
%3D
P(Y = 3|X = 3) =
(b) Are X and Y independent? (enter YES or NO)
(c) Compute the following probabilities:
P(X+Y > 2) =
%3D
P(XY = 2) =
P(주> 1) =
%3D
Transcribed Image Text:The joint probability mass function of X and Y is given by p(1, 1) = 0.4 p(1, 2) = 0.1 p(1,3) = 0.05 p(2, 1) = 0.05 p(2, 2) = 0.05 p(2,3) = 0.05 p(3, 2) = 0.1 p(3, 1) = 0.1 p(3,3) = 0.1 (a) Compute the conditional mass function of Y given X = 3: P(Y = 1|X = 3) = P(Y = 2|X = 3) = %3D P(Y = 3|X = 3) = (b) Are X and Y independent? (enter YES or NO) (c) Compute the following probabilities: P(X+Y > 2) = %3D P(XY = 2) = P(주> 1) = %3D
The distribution of heights of adult men in the U.S. is approximately normal with mean 69
inches and standard deviation 2.5 inches. Use what you know about a normal distribution and the 68-
95-99.7 rule to answer the questions in parts (a),(b),(c) below.
Your answer must be entered in the correct format. If your answer is a percent, such as 25 percent,
enter: "25 PERCENT" (without the quotes). If your answer is in inches, such as 10 inches, enter: "10
INCHES" (without the quotes and with a space between the number and the INCHES). If your answer
is an interval, such as 14 to 15 inches, then enter: "14 TO 15 INCHES" (without the quotes). Don't
report accuracy greater than what comes from the 68-95-99.7 rule! For example, if the rule says
"10 INCHES then "10.0 INCHES" is wrong because the extra decimal place claims too much
accuracy. If the rule says "1.2 INCHES" then "1.20 INCHES" is wrong.
(a) About what percent of men are between 69 and 74 inches?
Answer: .48
(b) Fill in the blank: About 2.5 percent of all men are shorter than
Answer: .67
(c) About what percent of men are taller than 69 inches?
Answer: 1/2
Transcribed Image Text:The distribution of heights of adult men in the U.S. is approximately normal with mean 69 inches and standard deviation 2.5 inches. Use what you know about a normal distribution and the 68- 95-99.7 rule to answer the questions in parts (a),(b),(c) below. Your answer must be entered in the correct format. If your answer is a percent, such as 25 percent, enter: "25 PERCENT" (without the quotes). If your answer is in inches, such as 10 inches, enter: "10 INCHES" (without the quotes and with a space between the number and the INCHES). If your answer is an interval, such as 14 to 15 inches, then enter: "14 TO 15 INCHES" (without the quotes). Don't report accuracy greater than what comes from the 68-95-99.7 rule! For example, if the rule says "10 INCHES then "10.0 INCHES" is wrong because the extra decimal place claims too much accuracy. If the rule says "1.2 INCHES" then "1.20 INCHES" is wrong. (a) About what percent of men are between 69 and 74 inches? Answer: .48 (b) Fill in the blank: About 2.5 percent of all men are shorter than Answer: .67 (c) About what percent of men are taller than 69 inches? Answer: 1/2
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