Let X1, X2,... be independent Exponential (3) random variables and Z = } E=1 X;. If Mz (t) is the mgf of Z then Mz (10)

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Q: how to find E(X), E(Y), E(X^2)

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A: Solution-: Given: n=3,p=2/5 ∴X→B(n=3,p=2/5) The p.m.f. of X is given by,  P(X=x)=3x*(25)x*(35)3-x…

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A: given  X~N5,2  the  z=X-μσ~N0, 1    mean = 5     variance = 2      ,   a) PX >2=PX-μσ>2-52…

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A: Expected value is used for discrete or continuous probability function. It is calculated by the…

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Q: If 'b' is Constant and X be a Random Variable then VX +b)3V(X)

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Q: Ex//let xa random variable with pm f p X=xN N , x=1,2,.., N and let Y=a+bx where a, bER find Ey and…

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Q: Find the mean and variance for the probability distribution given by f(x)= 2x k(k+1)* -,x=1,2,3,...k

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Q: Q. 1 (i) Find moment generating functions (mgf) of the following probability distributions. (ii)…

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A: From the given information, The population mean is m. The population variance is 10.…

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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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Q: If P(B) = ³/ and P(A'^B)= 1, for two events A and B, find P(A/B).

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Q: Prove that the variance of b, V(b) = o²(X'X)−¹

A: Given that We have to show that Var(b)=σ2(X'X)-1

Q: Page 327, 5.1.7.* Let X₁, ...,Xn be iid random variables with common pdf f(x) exp{-(x-20)}, x > 20,-…

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Q: Find the joint probability function of (X,Y) where

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Q: Suppose X, Y and Z are independent random variables with var (X) = 4 , var (Y) = 4 , var (Z) = 1/n…

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Q: Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate…

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A: It is given that the null hypothesis false. That is, it should be rejected.

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Q: Suppose X1,..., X, are iid exponential random variables with mean A Let Y, < Y, < •...< Y, be order…

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

Q: px (k) = c( (4)* k for k = 1,2,3,.. 3. Let X be a discrete random variable with %3D 3 A. Find the…

A: A) The value of c is calculated as follows: ∑1∞c13k=1c∑1∞13k=1 c13+132+133+...=1 c31+13+132+...=1…

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A: To show that an unbiased estimator of the risk of the James-Stein estimator iswe can use the…

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Q: Suppose that a random variable X has normal distribution with mean µ = 2 and variance σ 2 = 9, that…

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Q: 4), X2 ∼ N(μ = 1, σ^2 = 16), and X3 ∼N(μ = −4, σ^2 = 9). Let X1, X2, and X3 be independent and Y =…

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A: Given that  μx=70 , σx2=36   Variance of constant term is zero

Q: Suppose X1,X2,...,X, from a real-valued random variable X with unknown mean µ and standard deviation…

A: Suppose X1,X2,X3,.....Xn from a real-valued random variable X with unknown mean µ and standard…