A random variable X has a distribution with probability function f(x) = K(nx)2x for x = 0,1,2,...,n where n is a positive integer.
A random variable X has a distribution with probability function f(x) = K(nx)2x for x = 0,1,2,...,n where n is a positive integer.
a. Find the constant k.
b. Find the expected value M(S) = E(esX) as a function of the real numbers s. Compare the values of the derivative of this function M'(0) at 0 and the expected value of a random variable having the probability function above.
c. What distribution has probability function f(x)? Let X1, X2 be independent random variables both with the probability function above. By explaining how this distribution is obtained, explain why Y = X1 + X2, must have a distribution of the same type (no calculations are required for this).
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