Let Z be a discrete random variable with ?(Z)0. Does it necessarily follow that E(Z^3)=0? If yes, give a proof; if no, give a counterexample.

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A: The moment generating function of x is given by: Mxs=EesX=13es+23e2s+0e3sMxs=13es+23e2s

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Q: Show that the random variable X = Z and Y = 2?. fact that they are statistically dependent. are…

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Q: Find the nth moment of uniform random variable and hence its mean.

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Q: Assume that the frequency where a person acquires a fever in a month is given by a Poisson random…

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A: It is an important part of statistics. It is widely used.

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Q: ntinuous random variable

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Q: Let Xi. X2 --- Xn be a random sample from the Poisson _ 8*e¯® distribution . with pmf fix;o)=. Find…

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Q: Derive the variance of a Poisson random variable with parameter λ. [Hint. Start with the…

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Q: Xí,..., Xn are independent Poisson random variables with mean \, Find UMVUE for 2.

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Q: Verify central limit theorem for the independent random variablesX,, where for each k, P{X =± 1} = .

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Q: i) Let X,X2, be two identical independent distributed (iid)random variables ,each X- X2 having chi –…

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Q: 2. Let X1, X2, ..., X, be iid random variables with a common pdf/pf f(x, 0) depending on an unknown…

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Q: Let X be a discrete random variable with expectation -0.5 and variance 3. Let Y=−2X+8, find the…

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Q: Suppose the random variable X follows an Inverse Gaussian distribution with parameters u and 8. Use…

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Q: Let X and Y be random variables having the same distribution. Show that Cov(X +Y, X – Y) = 0. |

A: Given that  X and Y are same distribution thenE(X2)=E(Y2) , E(X)=E(Y) Show that Cov(X+Y,X-Y)=0

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Q: Let {Xi}ni be IID from Uniform(θ,0). Find the likelihood function and the MLE of θ

A: It is known that, Xi~ U(θ,0)  P.d.f. of uniform distribution, f(x)= 1/(θ-0) ;     0<x<θ = 1/θ…