If X1, X2, ... , Xk have the multinomial distribution ofDefinition 8, show that the covariance of Xi and Xj is−nθiθj for i = 1, 2, ... , k, j = 1, 2, ... , k, and i Z j.

Q: If X is uniform distributed over (0, 10), calculate that (i) P(X 7) (iii) P(1 < X < 6).

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Q: Consider the information below relating to the monthly rates of return for two companies X and Y…

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A: Given X~N2μ, Σ where μ=μμ and Σ=10.50.51

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A: c) Given that X1,X2,.....,Xn be independent such that Xi|p~Bernoulli (p). f(Xi|p)=pxi(1-p)1-xi…

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Q: Let pX(x) be the pmf of a random variable X. Find the cdf F(x) of X and sketch its graph along with…

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Q: (ii) If X is a Poisson distribution such that 2 P(X = 0) + P(X=2) = 2P(X= 1). find E(X). %3D %3D

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Q: 5. Suppose that (X,Y) is a point chosen uniformly at random from the triangular region formed by…

A: Solution :

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Q: If a is uniformly distributed over [-18, 30], what is the probability that the roots of the equation…

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Q: :If Z = ax + by and yis the correlation coefficient between Xand Y. Show that (a) o = a°o% +b²o…

A: Solution for this question is as given:

Q: Let X1, X2, ..., Xn be an independent random sample from n(µx,ox), and Y1, Y2, . .., Ym be an…

A: Given X1,X2,...,Xn~N(μx,σx2)Y1,Y2,....,Yn~N(μy,σy2) are two independent random samples.   Denote…

Q: Suppose that X is normally distributed with u = 10 ando 2. Find P(IX 10|S3)

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Q: Let X1,.,Xn be i.i.d with n 2 6, E(Xi) > 1 and Var(Xi) > 0. X1x2 and X3X5 are then. (A) not…

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Q: Suppose X, Y and Z be random variables with j.p.m. f. f(x, y, z)= kxyz with x E {1,2}, y = {1, 2,…

A: Given information: The value of k is obtained below:

Q: If a random variable X has a discrete uniform distribution. fx(x)=1/k for x=1,2,..,k;0 otherwise.…

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Q: a) X, is Gaussian with a mean of0.5 dolai 6) X, -2 dolars with pnbabibidty os, with probalai litty…

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Q: Let X, Y, and Z be random variables, and let Cov(-,;) denote the covariance operator as usual.…

A: GivenV(X)=0.7Cov(X,Y)=0.4Cov(X,Z)=1.2Cov(Y,Z)=0.8

Q: Let X be uniformly distributed over (0,4). Calculate E[X5].

A: Given: X follows Uniform distribution over ( 0 , 4)

Q: Calculate the covariance and correlation between X and Y. dint: Use the computational formula to…

A: Solution: The joint PMF of (X, Y)   value of Y    14 22 30 40 65 Total  Value of X 1 0.02…

Q: 36. Show that if X and Y are identically distributed, not necessarily indepen- dent, then Cov(X + Y,…

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Q: Let X1,· , Xn be iid with population density x > 8, fx (x) = {de- otherwise. Here d,0 are unknown…

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A: Given that the independent random variables X1 and X2 follows χ22 distribution.

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Q: - If a random variable X has a discrete uniform distribution fx(x): 1 for x = 1,2, ..., k; 0…

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Q: If X is uniformly distributed over (1, 2), find z such that P[ X >z + Hx] = ¼.

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Q: Suppose W ~ N(µ1, o}), and U ~ N (42, 03) with Cov(W,U) = 012. Let Y = a + bW and Z = b+ aU. 1)…

A: From the given information, W~Nμ1, σ12U~Nμ2, σ22CovW,U=σ12 Let Y=a+bW and Z=b+aU. 1. The…

Q: y 1 2 4 8 16 p(y) 0.05 0.10 0.35 0.40 0.10

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Q: Suppose the true model is given by Y = B(U)X +U where U - X and 8(U) = 1 if U >0 and =-1 if U < 0.…

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Q: T= inf{n>0: Xn = Xo}. = (i)sism is a stationary distribut. al on Xo has the distribution (and

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Q: 8.51 For an F-distribution, find (a) fo.os with vị = 7 and v2 = 15; (b) fo.os with vị = 15 and v2 =…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

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Q: If x is Uniformly distributed over the interval (1,2) and p(x > z+ ) = 1 then Z equal:

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Q: Let X~N, (u, Σ) 1. size n = 10 with μ' = (5 -2 4) 6 5 -3 Σ= 5 7 0 -3 0 4 find the distribution of X,…

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Q: Suppose that X1, . . . , Xn form a random sample from the uniform distribution on the interval [θ1,…

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Q: 8. Let X and Y be random variables and let A e B. Prove that the function JX (w), if w e A, Z (w) Y…

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Q: if x,x2, ... .., Xp be a random sample from Bin( 1,0). Show that T =i is UMVUE

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Q: Let X1, X2, Xn be continuous iid random variables with pdf f(x). The pdf of Yn= max(X1, X2, .. Xp)…

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Q: Suppose that, as in Exercises 5.11 and 5.79, Y1 and Y2 are uniformly distributed over the triangle…

A: The given diagram is,  Therefore, from this diagram,  The point are, (0,1),(-1,0),(1,0) i.e.…

Q: Let pX(x) be the pmf of a random variable X. Find the cdf F(x) of X and sketch its graph along with…

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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.