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## Homework Statement

Let X1, X2, X3,...Xn be independent and indentically distributed with pdf

f_X(x)= 4x^3 for 0 < x < 1

First I had to calculate the joint pdf of distribution of X1, X2, X3..Xn which I did

I got

4(X1*X2*X3*...*Xn)^3

Which I'm hoping is correct.

a) determine the probability that the first observation X1

is less than 0.5

b) determine the probability that ALL observations are less than 0.5.

c) use (b) to deduce then that the probability that the largest observation is less than 0.5

## Homework Equations

I've worked out the joint pdf which is 4(X1*X2*X3*...*Xn)^3

But I'm not sure what value I can plug into find out the probability because there are so many X's? Can anyone point me in the right direction? THANKS :)