P(X<Y)= P(X<t and t<Y) ----> t is [0,1]

=P(X<t)P(t<Y)

P(X<t)=t;

since P(Y<t)= $\displaystyle t^2$

P(t<Y)=1-$\displaystyle t^2$

so P(X<Y)= t(1-$\displaystyle t^2$)

am i right???? or the answer should be a numerical value?

Question2

(a)

i know that i have to find P(Z<t), then differentiate P(Z<t) to obtain

the density function of Z.

where P(Z<t)=P(min(X1,X2...Xn)<t)

=1-P(X1>t)P(X2>t)...P(Xn>t)

=1-[1-P(X<t)]^100-----@

finally use the density function of Z to find the 1st moment and 2nd moment ...

so as to find the mean and variance...

however , the process of differentiating @ is so complicated...

any one show the details...?