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**somestudent2** Suppose Y has density function:

f(y) = ky(1-y) when 0<=y<=1

and

f(y)= 0 elsewhere

[snip]

c)Find P(Y<=0.4|Y<=0.8)

d)Find P(Y<0.4|Y<=0.8)

[snip]

c) d) is where I have the problem. I suppose both must have the same answer.

Since this is conditional probability can we state that:

P(Y<=0.4|Y<=0.8) = [P(y<=0.4) AND P(y<=0.8)]/P(y<=0.8) = P(0.4<=Y<=0.8)/P(y<=0.8)

so I find using integral P(0.4<=Y<=0.8)=0.544

and P(y<=0.8) = P(0<=y<=0.8)=0.896

then we divide 0.544/0.896= 0.607

I feel that I am doing something wrong here, but can't see what.