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: 2. Suppose Yı. Y2. Ys, and Ya are mutually independent and identically distributed exponential…

A: Given  Yi~exp(1), i=1,2,3,4

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: (6) Let X be a Poisson random variable with parameter 0, then E(X²) = 1. От OF

A: Poisson distribution is the type of discrete probability distribution. It explain the number of…

Q: State with parameter(s) the probability distribution of Y = X₁ + X₂.

A:

Q: D. Assume that X1,X2, ..., X9 is a random sample from a r(1,0) distribution - The moment generating…

A: Solution

Q: Let X1, X2, , X36, be independent random variables such 5. that if 0 e1º). fx(x) = 1 36 (a) 1 –…

A:

Q: My(t) = 0.4e-¹ + 0.1 +0.5et Determine the probability that Y is equal to 0. Compute the variance of…

A: It is given that a discrete random variable Y has the moment generating function is:(t) = 0.4e-t +…

Q: (Q42) Let X and Y be independent Poisson random variables with X~ Poisson Y ~ Poisson (1)…

A: Let X and Y be independent Poisson random variables with X ~ Poisson (2) and Y~ Poisson (1)…

Q: Let X be a random variable with distribution function F(x) = 1-e*,x > 0, then the p.d.f of X is

A: Here given cumulative distribution function of x

Q: Suppose X and Y are random variables where Var(X)=8 and Var(Y)=6. If X and Y are independent, then…

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

Q: d) The random variable X has a Poisson distribution such that P(X= 0) = P(X = 1). Calculate P(X =…

A: Given problem Given that   d)   The random variable X has a Poisson distribution such that P( X=0…

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

A:

Q: Let M and N be two independent events such that P(M) = 1/3 and P(N) = 1/4. Find P(M/N')

A:

Q: (42) Let X be a random variable with p.d.f. ke 0<x<0 f(x) ={ find k. O.W

A: Given : f(x)=ke-23x                    0&lt;x&lt;∞

Q: (40) Let X be a random variable with p.d.f. (k +4)e¯3x f(x) ={ 01) O.w

A: a)Use the condition of valid pdf to find the value of k…

Q: (6) Let X be a Poisson random variable with parameter 9, then E(X²) = 1.

A: Given X~Pois(θ)

Q: Q5. A continuous r.v. X is said to have a Gamma (a, B) distribution if its moment generating…

A:

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

A:

Q: 4. Let X and Y be independent random variables with gamma distributions, r(3,2) and I'(4,2),…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Let Z and Y be discrete random variables taking values 0 with the corresponding distributionms P(Z =…

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

Q: 2. Let U1, U2,... be independent random variables, each with continuous distribution that is uniform…

A: The problem can be solved using the concept of expectation and moment generating function.

Q: uppose A1,A2,A3 dependent generating functions, Mx, (t) = e², Mx₂ (t) = ²t + t², and Mx, (t) = (² a)…

A: X1,X2,X3 are mutually independent random variables

Q: generating functions shown below. For each random variable also indicate what the mean and the…

A: We know that the moment generating function uniquely specify the distribution. Note : According to…

Q: 2X₁ Find the value of T such that P(Y>T) = 0.005, for Y =

A:

Q: A large cable company reports the following. 80% of its customers subscribe to its cable TV…

A: Given , P( cable TV) = 0.8 P( Internet service ) = 0.42 P ( telephone service  )= 0.37 P( cable TV…

Q: Let X1, X2, ... Xn random variables be independent random variables with a Poisson distribution…

A: Let x1 , x2 ......xn random variables be independent random variables with a Poisson distribution…

Q: Let (X1, ., Xn) be a random sample from the following discrete distribution: 2(1 – 0) P(X1 = 1) =…

A:

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

A:

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

A:

Q: 2. Find the distribution of the random variables that have each of the following moment generating…

A: We know, for a discrete random variable, m(t)=E[etX]=∑x=0∞etxP[X=x]=P[X=0]+etP[X=1]+e2tP[X=2]+....…

Q: 9. A discrete random variable X has the probability mass function given by a(T, x-1, 2,. -=(x)/…

A:

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

A:

Q: 4. Let X be a random variable following a binomial distribution with the following moment generating…

A:

Q: Let X and Y be independent random variables with gamma distributions, T(3,2) and (4,2),…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: (40) Let X be a random variable with p.d.f. (k +4)e-3* f(x) =- 01) O.w

A:

Q: E estimator c onal distribut us part, find

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: (4) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x)= , find E(e2x) O.w

A: Random Variable: A random variable is a real valued function that assign a real number to each…