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06-06-2023
Mathematics

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Consider X Gamma(a, p). (a) (5 pts) Find My(1), the mgf of X. For what values of 1 is it defined? (b) (5 pts) Use the moment-generating function to compute E(X). (c) (5 pts) Use the moment-generating function to compute var(X). (d) (5 pts) If c> 0, what is the distribution of Y = cX?

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