Let X has Poisson distribution with parameter A such that P(X=2) =9P(X=4) +90P(X=6). Find the value of parameter

Q: Let X = b(8,) find E(5+6x) and distribution function.

A: 3) From the given information, X≈b(8, 14) E(X)=8*14=2 Consider, E5+6x=5+6E(X)…

Q: Find the PSD of a stationary random process for which Auto correlation is RYx (t) 6 e- alt|

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Q: Let X be a random variable with pdf f(x) = kx*,-1 <x< 1. Find E (X).

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Q: Let X be a continuous random variable whose moment generating function is 4x(t) = (³.) ³. Find Var…

A:

Q: The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34.…

A: Formula used Var ( X+Y) = Var(X)+Var(Y)+2Cov(X,Y)

Q: Let X1, X2, .,X, be a random sample from S(x;0) = (0+1)xº 0<x <1 Find the method of moments…

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Q: Let X b(16, find E(4-3x) and distribution function.

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

Q: If X is a Poisson variable such that P(X= 2) = 9P(X = 4) + 90P(X=6), find the mean and variance of…

A: Let X be the random variable from Poisson distribution  with P(X=2) = 9P(X=4) + 90P(X=6)  Then,  We…

Q: f the random variable X follows the uniform distribution U= (0,1) What is the distribution of the…

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Q: A random variable x follows continuous uniform distribution on the interval [18,38]. Find the…

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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: i) Find the cumulative distribution function (CDF) of X. 8 ii) Show that the moment generating…

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Q: Let x be a continuous random variable with PDF 3 x > 1 x4 fx (x) otherwise Find the mean and…

A: Given PDF is fX(x) = 3x4,x ≥ 10,otherwise

Q: Suppose that the random change in value of a financial asset is X over the first day and Y over the…

A: The variance of X+Y is calculated asVarX+Y=VarX+VarY-2CovX,Y

Q: Let X1, . . . , Xn be iid from Exp(β). Find the distribution of the sample maximum Y = X(n) . Is…

A: Given that , , . . . . ,  be i.i.d. exponential with parameter .i.e.

Q: Let Y₁, Y2,..., Yn denote a random sample of size n from a population with a uniform distribution on…

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Q: If Y is a standard Cauchy random variable, show that Y and are identically distributed. Y

A: Solution

Q: The number of clients a store has during a week is Poisson distributed with mean A = 25. The amount…

A: The moment generating function is, ϕt=e1000t+250t2 Mean: Et=ddtϕt   by putting t=0…

Q: (1) Let X b(16, find E(4-3x) and distribution function.

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Q: (47) Let X b(8, -) find E(5+6x) and distribution function.

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Q: Let X₁, X2, ..., X₁ be a random sample from a population with cumulative distribution function F(x)…

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Q: Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.

A: Solution

Q: Let X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y =…

A: X~ Uniform (-2,2)  Then we have to find pdf of Y=X5

Q: 3. Let X, Y be two random variables. Suppose X ~ Unif(0, 1)), and Y|X = 1 ~ Unif((0, e-)). (a) Give…

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Q: The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is…

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Q: Let X1 and X2 be IID exponential with parameter  &gt; 0. Determine the distribution ofY = X1=(X1 +…

A: Consider the random variables, (X1+X2)~Exp(λ) The CDF of Y=X1+X2 is,

Q: Use the geometric distribution to derive E(Y), E(Y^2), and V(Y) from the Poisson distribution

A: The geometric distribution and Poisson distribution are two different types of probability…

Q: Find the mean of random variable of X, if X is random variable with pdf f(x) = c(1-x²), -1<x< 1and 0…

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Q: (13) Let X b(6,) find E(5+6x) and distribution function.

A: (13) The random variable X follows binomial distribution with sample size 6, and probability of…

Q: Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is

A: From the given information, the joint density function for X  and Y is,

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.