"The continuous random variable X has pdf f(x) = 1 0<x<1. X1,X2,X3 are independent random variables all with the same distribution as X. Y = max{X1,X2,X3} and Z=min{X1,X2,X3}. Find E[Y-Z]."

I have a quick question regarding how to solve for E[Y] and E[Z]...

Solution was to solve the cdf in order to solve for E[Y] and use the survival function to solve for E[Z].

Is this always the case when you are dealing with max and min with respect to random variables such as above?

max -> use cdf

min -> use survival?

Best regards,

j

I have a quick question regarding how to solve for E[Y] and E[Z]...

Solution was to solve the cdf in order to solve for E[Y] and use the survival function to solve for E[Z].

Is this always the case when you are dealing with max and min with respect to random variables such as above?

max -> use cdf

min -> use survival?

Best regards,

j

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