Question

suppose that x is a continuos randoms variable with pdf given by f(x) = x³ / 4 for 0 less than or equal to x less than or equal to 2. Consider random variables defined by function Y= square root of x

1) what is the support of y?

2) graph y as a function of x

3) give pdf of y

4) what is expected value of y

Answer 1

1)

The support of x is [0,2]

Thus, the support of y is the interval :

2)

The graph of y as a function of x is given by:

3)

The cdf of y is given by:

Thus, the pdf is given by:

4)

The expected value of y is :

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