Exercise 3.13 (Gamma Distribution) Suppose that a continuous random variable has the density function where (x) is
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Exercise 3.13 (Gamma Distribution) Suppose that a continuous random variable has the density function
where Γ(x) is the gamma function (3.21). Prove that the MGF is given by
Using this, show that E[X] = α/λ and V[X] = α/λ2. Note: An exponential distribution is a special case with α = 1, while the case with α = n/2 and λ = 1/2 corresponds to a chi-square distribution with n degrees of freedom.
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Stochastic Processes With Applications To Finance
ISBN: 9781439884829
2nd Edition
Authors: Masaaki Kijima
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