Let X be the number of trials until the r -th success in a sequence of independent Bernoulli variables with probability of success p Give the limiting moment generating distribution of Y = pX as p → 0 evaluated at t = 0,3 and r = 6

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Let Y₁,..., Yn be an iid sample U(0, 0), 0 > 0, with pdf { 1/0, 0≤ y ≤0, 0, elsewhere and CDF f(y) = F(y) = = 0, y < 0, y/0, 0≤ y ≤ 0, 1, y ≥ 0

Suppose you are given the moment generating function M(t) =- e for t< In 4-3e Find the mean and variance of this distribution.

Let X∼Uniform(0,1) distribution. Find the PDF of Y= 3√X and derive the expected value and the variance of Y.

(17') The random variable X obeys the distribution Binomial(n,p) with n=3, p=0.45. (a) Write Px(1), the PMF of X. Be sure to write the value of Px(T) for all z from -o to +oo. (b) Sketch the graph of the PMF Px[x]. (c) Find E[X], the expected value of X. (d) Find Var[X], the variance of X.

What is the critical value for a two-tailed t test when α = 0.02 and d.f. = 18?

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Find the value of P(X=1),for a binomial distribution where mean is equal to 3 having 6 trails.

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