Question

Asked Oct 25, 2019

Show that Y has a CDF that is U(a,b).

Step 1

a.

Show the graph of the probability density function of Uniform distribution.

From the given information, the random variable *X* be a uniform random variable, U(*a*,*b*) and its probability density function is f(*x*)=1/(*b*-*a*)

The graph of the probability density function is,

Step 2

b)

From the given information, *Y*=(*b*-*a*)*Z*+*a* and *Z* is a standard uniform random variable U(0,1).

The probability density function for *Z* is, f(*Z*)=1/(1-0)=1. The mean for Z is 1/2 and the variance for *Z* is 1/12.

The mean for *Y*=(*b*-*a*)*Z*+*a* is,

Step 3

The variance for *Y*=(*b*-*a*)*Z*+*a* is,

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