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
distribution of Z - X + Y
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