= Zn be a Poisson random variable with parameter = n. Let Yn = (Zn-n)/√n. Show t Yn converges in distribution to a standard normal random variable Z~ N(0, 1). Note t the mgf of Zn is m(t) = en(et-1) and the mgf of Z is et²/2

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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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A: Given that  fx=3x2, 0&lt;x&lt;1 Consider, μ=∫x=01xfxdx  =∫x=01x*3x2dx =3x4401  =34 σ2=∫x=01x2fxdx-μ2…

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A: As per bartleby guidelines we can solve only first question and rest can be reposted

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A:

Q: Let X be a discrete random variable having the Poisson distribution with parameter u. we know that…

A: Let X be a discrete random variable having a Poisson distribution with parameter .We know that .

Q: Let X be a discrete random variable having the Poisson distribution with parameter μ. we know that…

A: Let X be a discrete random variable having a Poisson distribution with parameter μ.We know that…

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A:

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A:

Q: The Gamma pdf for continuous random variable Y takes the form 1 -ya-le-ylß B«T(a)" y > 0 fV) = for…

A:

Q: None

A: Step 1:Step 2:Step 3:Step 4:Option(E) : correct

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A:

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A: To estimate the probability distribution from x1 = -2 up to x2 = 1.6 using Romberg Integration, we…

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A: The answer is given using the concept of likelihood.

Q: Suppose that Y Еxponential() ~ and let X = exp{-Y/ß} be a new continuous random variable. If…

A:

Q: The Gamma pdf for continuous random variable Y takes the form 1 va-le-y/ß -lB y > 0 f(y) = βαΓ (α) "…

A: Given that Y has Gamma distribution with α=3 and β=1.6. Consider,…

Q: y > 0 fV) = for ß > 0. y 1.9) Give your answer to three decimal places.

A:

Q: Let X be a random variable and a real number. Show that E(X - a)² = varX + (µ − a)² Hereμ = EX is…

A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

Q: Show that #z=0.

A: Suppose the random variable Y has a mean of 21 and a variance of 36. Let Z=( 1 /√36)(Y-21)

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A: We have to find the log likelihood function for the normal distribution.

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Q: Find the variance by calculating the first two moments of the random variable X = (- 1 / λ) ln…

A: For U~u(0,1) pd.f. of U is f(u)= 1, 0&lt;u&lt;1 To find mean and variance we find p.d.f. of X.

Q: Let X and Y be jointly Gaussian random variables with sigma X = 11, sigma Y = 5and E [XIY] = 11/20…

A: Given that and  be jointly Gaussian random variables, with ,  and

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Q: Let X1, X2,..., X, be a set of independent random variables each following the distribution with pdf…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

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Q: et X1, X2,..., Xn be a random sample of size n >3 from a normal distribution ith unknown mean μ and…

A: Variance equal to 2.

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A: Let w1, w2......wt be independent random variables from a normal distribution with mean 0 and…

Q: Let X = ((X,,Y),....(X, Yn)) be a sample from a bivariate normal population. how that the…

A: Given information: It is given that X be a sample from a bivariate normal population.

Q: 4, ELY Suppose X and Y are two random variables with E[X] = 1, Var (X) Var (Y) = 4, and Cov (X, Y) =…

A: Var(X)=4, Var(Y)=4, Cov(X,Y)=1