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5. Let X be a Poisson random variable with parameter λ = 6, and let Y...
Let X be a Poisson random variable with parameter λ = 6, and let Y = min(X, 12). (a) What is the p.m.f. of X? (b) What is the mean of X? (c) What is the variance of X? (d) What is the p.m.f. of Y? (e) Compute E[Y ].
5. Let X be a Poisson random variable with parameter λ 6, and let Y-min(X,12 (a) What is the p.m.f. of X? (b) What is the mean of X? (c) What is the variance of X? (d) What is the p.m.f. of Y? (e) Compute E[Y].
5. Let N be a Poisson random variable with parameter λ. Suppose ξι, ξ2, is a sequence of 1.1.d. random variables with mean μ and variance σ2, independent of N. Let SN ξι + ξΝ. Determine the mean and variance of SN.
Show all details: Exercise 10.4. Let X be a Poisson random variable with parameter λ. That is, P(X = k) e-λλk/kl, k 0.1 Compute the characteristic function of (X-λ)/VA and find its limit as Exercise 10.4. Let X be a Poisson random variable with parameter λ. That is, P(X = k) e-λλk/kl, k 0.1 Compute the characteristic function of (X-λ)/VA and find its limit as
Let X be a Poisson random variable with mean λ(a) Evaluate E{X(X −1)} from first principles, and from this, the variance of X. (b) Confirm the variance using the moment generating function of X.
Let N be a Poisson random variable with parameter λ. Suppose ξ1,ξ2,... is a sequence of i.i.d. random variables with mean µ and variance σ2, independent of N. Let SN = ξ1 + ...ξN. Determine the mean and variance of SN
Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X is r E 0,1,2,...) This distribution is often used to model the number of events which will occur in a given time span, given that λ such events occur on average a) Prove by direct computation that the mean of...
please help me! Thanks in advance :) 5. Let N be a Poisson random variable with parameter λ Suppose ξ1S2, is a sequence of 1.1.d. random variables with mean μ and variance σ2, independent of N. Let SN-ξι 5N. Determi ne the me an and variance of Sw. 6. Let X, Y be independent random variables, each having Exponential(A) distribution. What is the conditional density function of X given that Z =
3, Let X be a Poisson random variable with parameter λ. Calculate the conditional expectation of X given that X is odd.
(a)Suppose X ∼ Poisson(λ) and Y ∼ Poisson(γ) are independent, prove that X + Y ∼ Poisson(λ + γ). (b)Let X1, . . . , Xn be an iid random sample from Poisson(λ), provide a sufficient statistic for λ and justify your answer. (c)Under the setting of part (b), show λb = 1 n Pn i=1 Xi is consistent estimator of λ. (d)Use the Central Limit Theorem to find an asymptotic normal distribution for λb defined in part (c), justify...