Let X be a random variable with pdff(x) = 4x^3 if 0 < x < 1 and zero otherwise. Use the cumulative (CDF) technique to determine the pdf of each of the following random variables: 1) Y=X^4, 2) W=e^(-x) 3) Z=1-e^(-x) 4) U=X(1-X)

Let X be a random variable with pdff(x) = 4x^3 if 0 < x < 1 and zero otherwise. Use the cumulative (CDF) technique to determine the pdf of each of the following random variables: 1) Y=X^4, 2) W=e^(-x) 3) Z=1-e^(-x) 4) U=X(1-X)

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

Section13.3: Special Probability Density Functions

Problem 30E

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Question

Let X be a random variable with pdff(x) = 4x^3 if 0 < x < 1 and zero otherwise. Use the
cumulative (CDF) technique to determine the pdf of each of the following random variables:

1) Y=X^4,

2) W=e^(-x)

3) Z=1-e^(-x)

4) U=X(1-X)

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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