It doesnt sound like Y and X are indep at all
Furthermore that would be E(YlX) not E(Y).
The time interval Y between successive feedings of a certain type of insect has an exponential distribution with mean proportional to a positive measured characteristic x of the insect. Suppose we observe n independent insects, observing time intervals Y1, . . . , Yn with associated characteristics x1, . . . , xn.
Let E(Y)=a.
I have need to calculate . I supposed they were independent and then using the information i have E(Y)=cX so I get a/(c/a)=a^2/c. I think however that it is wrong.