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It's hard to type this out as there is a diagram and notation I can't find on the key board so I've attached an image of the question and answer. I've explained my solution below however I've also attached an image if it's too confusing with the lack of symbols!

I figured that E(feta) = (0+(pi/2))/2

And that cos(feta) ~ U[0, 1]

So E(4cosfeta) = 4 x 1/2

This is incorrect and If I integrate 4cos(feta) x 2/pi I get the right answer but I don't know why the previous method dosent work?

b(ii) I did P(X<= 3) = P(cos(feta) <= 0.75) and then = 0.75 (by my previous calculation of cos(feta) ~ U..)

Also why is p(cos(feta) < 0.75) = P(feta => 0.732..) why does the sign switch??

**Problem involves uniform distribution and integration.**I figured that E(feta) = (0+(pi/2))/2

And that cos(feta) ~ U[0, 1]

So E(4cosfeta) = 4 x 1/2

This is incorrect and If I integrate 4cos(feta) x 2/pi I get the right answer but I don't know why the previous method dosent work?

b(ii) I did P(X<= 3) = P(cos(feta) <= 0.75) and then = 0.75 (by my previous calculation of cos(feta) ~ U..)

Also why is p(cos(feta) < 0.75) = P(feta => 0.732..) why does the sign switch??