Question: Let X be a continuous random variable such that f X (x )= (1+x /) +1 for x0 , with >0 and >2 . Note

Let X be a continuous random variable such that f X (x )= (1+x /) +1 for x0 , with >0 and >2 . Note that E( X )= 1 and Var ( X )= 2 (2)(1) 2 .

a) (2) Determine E( X 2 ) . Hint: don't integrate the density function, instead use what you know about the variance.

b) (4) Determine the method of moments estimators for and . (Be careful with your algebra.)

Let X be a continuous random variable such that f X (x

\f

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