3. Let X be a discrete random variable with probability mass function p(n) = 7 (1)", Find the moment-generating function Mx(t) with the appropriate domain. n = 1,2,3,....

Q: Let X be a discrete random variable with the following moment generating function: (1/2) e' M(t) - 1…

A: Solution: From the given information, the moment generating function is

Q: 1. Let X be a random variable with a probability distribution Pr(X=1)=0=1-Pr(X=-1), where 1/2 <0 <…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: X is a continuous random variable taking values between 0 and 2. If F(1.5) = 0.70 and P(X<1) = 0.20,…

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Q: Use the moment generating function you just proved to verify that for a Poisson distribution, E(X) =…

A: The moment-generating function (mgf) of a random variable X is given by                Mx(t)=E(etx)…

Q: 7. If X is a random variable with fx Let Y = 3√In X. (a) Fx(x) ) = 1, 1<x<e (b) Fy(y) (c) fy(y)

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Q: 12. Let a random variable X has a geometric distribution with p.d.f. f(x) = pq*", k =1,2,3,. Show…

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Q: C2. Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ =…

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Q: . Let Y be a continuous random variable where f(y) F(y)? (a) Y 18 Y 15 Y-3 18 y+3 (b) (c) (d) 18 (e)…

A: The random variable Y is a continuous random variable with pdf f(y) = 1/18 ; -3 ≤ y ≤ 15

Q: Suppose §1, $2, ... are iid random variables having mean u and variance o?. Form the random sum SN =…

A: Given that ξ1, ξ2, ..., ξn are iid random variables having mean μ and variance σ2.  SN=ξ1+ξ2+...+ξN

Q: 500 participants were asked what coping method they use to overcome poor mental health. The results…

A: A table is given : Total outcomes (N) = 500 Let A represents mindfulness activity B represents…

Q: Does this posterior distribution still belong to the Gamma distribution family? If so, what are the…

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Q: fx(x) = = ´7xºa¯¯exp ( − (²)²¹), if x ≥ 0; -7 - otherwise. 10, Find the maximum likelihood estimator…

A: we need to find the MLE of .

Q: 3. Let Y be the number of speeding tickets a YSU student got last year. Suppose Y has probability…

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Q: Let X be a random variable with E[X]=2, Var(X)= 4. Compute the expectation and variance of 3– 2X .

A: Solution-: Given: E(X)=2, Var(X)=4 Our aim to find, (a) E(3-2X)=? and  (b) Var(3-2X)=?

Q: Let X₁, , Xn be a random sample from a large population following a uniform distribution over [0,…

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Q: Derive the posterior distribution for 1 given (x1, ...,x7) up to a proportional constant.

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Q: 6. (a) Let X1 and X2 have independent distribution B(n1,p) and B(n2,p). Find the moment-generating…

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Q: 2. Let X and Y be two random variables. Suppose XY ~ Binomial (n, Y) where n is fixed and Y stands…

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Q: Consider the formula: P(x) = x2/21, x = 0, 1, 2, 4. Is P(x) a probability mass function? If so, show…

A: Solution: 9. From the given information,

Q: (16) The moment-generating function of the geometric random variable X with parameter p is M(t) =…

A: The moment-generating function of random variable X is given as, M(t)=p1-1-pet It is known that…