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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Theorem 6.4 states that the moment-generating function of the gamma distribution is given by Mx(t) = (1-βt)^(-α).Find the moment generating function ME(t) for an exponential random variable with parameter (lambda) = 1. Sketch the graph of ME(t)
- If X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval [a, b], what is the moment generating function of X + 2Y ?Let X1, X2, ... , Xn be a random sample from N(μ, σ2). Find the Moment Generating Function of X̅. If n = 16 and σ = 2, compute P(-1 ≤ X̅ - μ ≤ 1).Find the moment generating function of the continuous random variable X∼U (a, b).