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2 b-a a с b X 1. Let X be a random variable such that X Tr(-1,1,0). ~ a. Find the pdf of X, fx(x). b. Find the cdf of X, Fx (x) c. Find P(-/< X <-). d. Find E[X] e. Find Var[X] 2. With X as above, let Y = rX+s, where r and s are real numbers. (All answers to the following questions will be in terms of r, s). a. Find the cdf of Y, fy(x). b. Find the pdf of Y, Fy(x). c. Find E[Y] d. Find Var[Y]. e. Find the values of rs such that Y TrI5 15 101

2 b-a a с b X 1. Let X be a random variable such that X Tr(-1,1,0). ~ a. Find the pdf of X, fx(x). b. Find the cdf of X, Fx (x) c. Find P(-/< X <-). d. Find E[X] e. Find Var[X] 2. With X as above, let Y = rX+s, where r and s are real numbers. (All answers to the following questions will be in terms of r, s). a. Find the cdf of Y, fy(x). b. Find the pdf of Y, Fy(x). c. Find E[Y] d. Find Var[Y]. e. Find the values of rs such that Y TrI5 15 101

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 14E
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2 b-a a b X 1. Let X be a random variable such that X~ Tr(-1,1,0). a. Find the pdf of X, fx(x). b. Find the cdf of X, Fx(x) C c. Find P(-/ < X <). 2 d. Find E[X] e. Find Var[X] 2. With X as above, let Y=rX+s, where r and s are real numbers. (All answers to the following questions will be in terms of r, s). a. Find the cdf of Y, fy (x). b. Find the pdf of Y, Fy(x). c. Find E[Y] d. Find Var[Y]. e. Find the values of r, s such that Y~ Tr[5.15.101. 27
Transcribed Image Text:2 b-a a b X 1. Let X be a random variable such that X~ Tr(-1,1,0). a. Find the pdf of X, fx(x). b. Find the cdf of X, Fx(x) C c. Find P(-/ < X <). 2 d. Find E[X] e. Find Var[X] 2. With X as above, let Y=rX+s, where r and s are real numbers. (All answers to the following questions will be in terms of r, s). a. Find the cdf of Y, fy (x). b. Find the pdf of Y, Fy(x). c. Find E[Y] d. Find Var[Y]. e. Find the values of r, s such that Y~ Tr[5.15.101. 27
Vocabulary • Support of a random variable X: The set of values x such ● that the pdf of X is positive. • Mode of a distribution: the value x where the pdf is maximized. X Exponential (A) means that the random variable X has an exponential distibution with parameter 1 Here is a picture of the pdf of a triangular distribution Tr (a, b, c) whose support is (a, b) and whose mode is c
Transcribed Image Text:Vocabulary • Support of a random variable X: The set of values x such ● that the pdf of X is positive. • Mode of a distribution: the value x where the pdf is maximized. X Exponential (A) means that the random variable X has an exponential distibution with parameter 1 Here is a picture of the pdf of a triangular distribution Tr (a, b, c) whose support is (a, b) and whose mode is c
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