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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).B) Let the random variable X have the moment generating function e3t M(t) for -1(6) Let X be a Poisson random variable with parameter 0, then E(X²) = 1. От T O FLet X be a discrete random variable with P(X = -1) = .3, P(X = 1) = .45, P(X = 2) = .15 and P(X = 6) = .1. Find Var(X).Suppose that a random variable X is an Exponential Random Variable with parameter β = 3.(a) What is E(X)?(b) Compute P(X > 2).(c) Compute P(X > 5 |X > 3).If a random variable X has the moment generating function Mx (t)= 2 - ť Determine the variance of X.Let X be a random variable such that E(X²) a. V(3X-3) b. E(3x-3) = 58 and V(X) = 40. ComputeLet X1, X2, ..., X, be independent random variables and Y = min{X1, X2, ..., Xm}. Fy (y) = 1 – || (1 – Fx,(y)) i=1 (a) A certain electronic device uses 5 batteries, with each battery to have a life that is exponentially distributed with mean of 48 hours and is independent of the life of other batteries. If the device fails as soon as at least one of its batteries fail, what is the expected life of the device?Consider the random variable X such that E(X) = 3 and Var(X) = 2 if the random variable Z = 1+5X. E(Z) is what?(16) The moment-generating function of the geometric random variable X with parameter p is M(t) = 1-per. Use this to find the mean and variance of X.Q3/(a) Let X = b(n,) and E(x)= E(16-7x) find n. (b)Let X be a random variable with p.d.f, ƒ(x)= c 3 x=1,2,3,.., zero elsewhere. Find the constant c.