Question

In: Statistics and Probability

Problem 1 Let X1, X2, . . . , Xn be independent Uniform(0,1) random variables. (...

Problem 1 Let X1, X2, . . . , Xn be independent Uniform(0,1) random variables. (

a) Compute the cdf of Y := min(X1, . . . , Xn).

(b) Use (a) to compute the pdf of Y .

Solutions

Expert Solution

The cdf of the random variable X denoted by is given by

(a)

Y=min(X1,X2,...,Xn)

The cdf of Y is given by

(b)

The pdf fY(y) is obtained from (a) as:

(c)

The expectation of Y is given by

[n+1>0]

Hopefully this will help you. In case of any query, do comment. If you are satisfied with the answer, give it a like. Thanks

orchestra answered 1 year ago

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