Find P(μ – 20 < X < μ + 26).
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.If a random variable X has the moment generating function Mx (t)= 2 - ť Determine the variance of X.The moment generating function of the random variable X is given by mx(s) = e2e-2 and the moment generating function of the random variable Y is my (s) = (et + )10. If it is assumed that the random variables X and Y are independent, find the following: (a) E(XY); (b) E[(X – Y)²] (c) Var(2X – 3Y).
- Let X1 and X2be independent exponential random variables: fX1(x1) = e−x1 and fX2(x2) = e−x2 1If X is a Poisson variable such that P(X =2) = 9P(X= 4) + 90P(X = 6), find the mean and variance of X.Let 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?
- (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.Example 24: If a random variable X has the moment generating function Мx (t) — 2-t' determine the variance of X.Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).
- Let 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?B) Let the random variable X have the moment generating function e3t M(t) for -1Consider the random variable X such that E(X) = 3 and Var(X) = 2 if the random variable Z = 1+5X. E(Z) is what?SEE MORE QUESTIONS
