Consider a continuous random variable X with the probability density function (pdf):XC0< x≤2fx(x) =x² +1'0,otherwise.I(a) Obtain the constant c.(b) Calculate the cummulative distribution function (cdf) of X.t(c) Obtain the cummulative distribution function (cdf) and probability density func-tion (pdf) of the random variableY = 1/X.

a) The value of c is obtained below: ∫02fxdx=1∫02cxx2+1dx=1c*12lnx2+102=1c*12ln5=1 c=2ln5

Answered: Consider a continuous random variable 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

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 23E

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Consider a continuous random variable X with the probability density function (pdf) x 0< x≤2 fx(x) = otherwise. (a) Obtain the constant c. x² +1 I