Let X and Y be two independent random variables with moment generating functions M, (t) = e and M, (t) = e Calculate P(3 < X < 10). 2+28
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- The p.d.f. of a random variable X' is as shown in the figure. The pdf is zero for X 5. Calculate (i) the maximum value of p.d.f. (ii) expectation of X, E(X) (iii) variance of X. fx (x) kLet the random variable X have the moment generating function M(t) = e³t 1-t² = -1 < t < 1 What are the mean and the variance of X, respectively?The pdf of a random variable X is given by fx (x) 2If the pdf of a random variable X is f(x) = { 0.15-0.15(x-0.5), x ≥ 0.5 otherwise Find the moment generating function and use it to find the mean and variance of X.If Y is a random variable with moment generating function my (t) = e°, what is the mean of Y ?Q3. The moment generating function for a random variable X is M(t) = e³t 1-t2¹ What are the mean and the variance of X, respectively? -1 < t < 1.C1. Let X be a continuous random variable with PDF f(x) = (2-x) for -1 ≤ x ≤ c and f(x) = 0 otherwise. (a) Explaining your work, find the value of the constant c. (b) What is P(X > 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.Let X be a random variable normally distributed with mean μx 1. Find the mean μy of Y. 2. Find the standard deviation oy of Y. 3. Find the PDF fy of Y and evaluate fy (5). (My, oy, fy (5)) = ___________). = 6 and standard deviation ox = 4. Let Y = 4X + 5.Suppose W is a random variable with the pdf f(w) = 3u3e-w³/343 for w≥ 0.1 If Y = -12W + 11, what is the pdf of Y? еLet E and F be two events of an experiment, and suppose Pr(E)=0.3, Pr(F)3D0.2, and Pr( EF)-D0.15. Find each of the following probabilitles. Round answers to 2 decimal places, where needed. Pr( EUF) Pr( E') Pr( E' N F) Pr( E| F}O Let X be the random variable with probability law: P (X=r) = q' P; r=1, 2, 3,... Determine the moment generating function and hence mean and the variance. Assume P + q=1.5. Let X be a random variable with the PDF f(x) = r - 1| for 0 0.5) (c) Calculate E(X) and Var(X)SEE MORE QUESTIONS