 # 1. Assume X is Binomial(n,p), where the constant p € (0,1) and...

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1. Assume X is Binomial(n,p), where the constant p € (0,1) and the integer n > 0. (a) Express P(X > 0) in terms of n and p. (b) Define Y = n - X. Specify the distribution of Y. 2. Assume X is a random variable following from N(, o2), where o > 0. (a) Write down the pdf of X. (b) Compute E(X2). (b) Define Y - X-u Find the distribution of Y. 3. Suppose X ~ Beta (a, B) with the constants a, B > 0. Define Y = 1 - X. Find the pdf of Y. 4. Suppose X1, X2, X3~ exp(1) and they are independent. (a) Compute the cdf of X1. (b) Let Y - max (X1, X2, X3). Find the cdf of Y. (c) Derive the pdf of Y. 5. Suppose X ~ Poisson( (à = 5) and Y ~ Poisson ( - 10), and they are independent. Using the moment generating function method, find the distribution of Z - X + Y .

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