Suppose that X and Y are independent random variables each with a x'(2) distribution. Find the moment generating function of U = X+ 2Y. State clearly and justify all steps taken. Hint: You may use without proof the fact that the moment generating function of a x'(v) random variable W is v/2 ()". Mw(t) = - 2t
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- The moment generating function of the random variable X is given by mX(s) = e2e^(t)−2 and the moment generating function of the random variable Y is mY (s) =(3/4et +1/4)10. If it is assumed that the random variables X and Y are independent, findthe following:(a) E(XY)(b) E[(X − Y )2](c) Var(2X − 3Y)Calculate the mean and variance when the probability variable X's moment-generating function is as follows f(x)= 2x-1/16 , x=1,2,3,4 my answer is mean = 25/8, var = 170/16 - (50/16)^2 but solution is mean = 2, var = 4/5 How do we solve the problem? Help meSuppose that X is a random variable for which the moment generating function is as follows: MX(t) = e^(2t^2+3t) for −∞ < t < ∞. Find the mean and variance of X. (b) Suppose that X has moment generating function MX(t) =(3e^t/4 + 1/4)^6(i) Find the p.m.f. of X. (ii) Find the mean and variance of X. (c) A person with some finite number of keys wants to open a door. He tries the keys one-by-one independently at random with replacement. How many trails you expect, from him, to open the door? (d) Obtain the form of moment generating function (m.g.f.) for the following p.m.f. – p(x) = ((2^x)(e^-2))/×!, x = 0,1,2, … . Also calculate the mean and variance from m.g.f.
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- Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)Find the mean of the random variable X with PDF S 3x² _if 0If the random variable X follows the uniform distribution U= (0,1) What is the distribution of the random variable Y= -2lnX. Show its limits.Suppose Y is a random variable with E(Y) = 13 and Var(Y) = 6. Solve for the following: (show complete solution) a. E(3Y+ 10) = ? b. E(Y^2) = ? c. Var (10) = ? d. Var (5) = ?Suppose the random variable Y has a mean of 21 and a variance of 36. Let Z = √36 Show that #z=0. Show that o₂ = 1. (Y-21). #₂ = E(Y-D] -0--0 (Round your responses to two decimal places) o = var (Y-] )- (Round your responses to two decimal places)X = max(10,Y) with Y ~ Poisson(lambda=13) a) Calcuate the exact expectation and the variance of X.SEE MORE QUESTIONS