Question: Consider the gamma distribution function for stochastic variable X: and F(x)=0 for x (a) Find the characteristic function for this distribution. (b) Write the Levy-Khintchine

Consider the gamma distribution function for stochastic variable X:

F(x)= (4)" n/2 1 So F(n/2) dyy (1/2)-1-7/2 for x > 0

and F(x)=0 for x

(a) Find the characteristic function for this distribution.

(b) Write the Levy-Khintchine formula for the characteristic function. That is, find a and G(x). Is X infinitely divisible? [Hint: First find F(x) and use it to find Gy(x) and take the limit.]

F(x)= (4)" n/2 1 So F(n/2) dyy (1/2)-1-7/2 for x > 0

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