1)Let x be a uniform random variable over the interval (0, 1). Knowing that y = x2 , calculate: a)Determine Fy(Y) = P(y<=Y),Y real and determine the pdf of y. b)Calculate E[x2] , using the pdf of x. c)Calculate E[y], using the pdf of y and compare with part (b).

1)Let x be a uniform random variable over the interval (0, 1). Knowing that y = x2 , calculate: a)Determine Fy(Y) = P(y<=Y),Y real and determine the pdf of y. b)Calculate E[x2] , using the pdf of x. c)Calculate E[y], using the pdf of y and compare with part (b).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 21E

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Question

1)Let x be a uniform random variable over the interval (0, 1). Knowing that y = x² , calculate:

a)Determine F_y(Y) = P(y<=Y),Y real and determine the pdf of y.
b)Calculate E[x²] , using the pdf of x.

c)Calculate E[y], using the pdf of y and compare with part (b).

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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