that didn't make sense, that t stuff doesn't make sense
yes, it's a constant, this is just calc 3
The joint density is on the unit square
so your probability is the double integral over the appropriate region...
or the simpler by inspection
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)=
P(t<Y)=1-
so P(X<Y)= t(1- )
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...?