a) Suppose the height of a rectangle is twice its width and the width is a uniform distribution over [0,6]. Find the expected area of the rectangle.
b) Let X have m.g.f. of Mx(t) = (1-5t)^-2 for t<1/5. Find the Var(X)
a) Suppose the height of a rectangle is twice its width and the width is a uniform distribution over [0,6]. Find the expected area of the rectangle.
b) Let X have m.g.f. of Mx(t) = (1-5t)^-2 for t<1/5. Find the Var(X)
a) $\displaystyle A=HW=2W^2$
SO $\displaystyle E(A)=2E(W^2)={1\over 3}\int_0^6 w^2dw$
b) you can differentiate twice and let t=0 to get the first two moments
From that you can get the variance.
However this is a gamma and you can obtain the variance by inspection.