Hey perh.
Hint: For these problems, use the definition of expectation (and variance) in integral form. For c) I'd suggest looking at the MGF of the expectation of the transformed variable and compare it to a known table of MGF's.
Let X~N(μ,σ^2).
Determine
(a) Compute E[(X-μ)^4)]
(b) Compute E[|X-μ|]
(c) Define Y = (X-μ)^2. Determine the distribution of Y, and find the expected value of 1/Y.
At the first time, I thought that E[(X-μ)^4)] is same with Var(X^2). Is it true?
And how can I solve the other problems?
Hey perh.
Hint: For these problems, use the definition of expectation (and variance) in integral form. For c) I'd suggest looking at the MGF of the expectation of the transformed variable and compare it to a known table of MGF's.