If X is a Poisson variate such that P(X = 1 3/10 and P(X = 2) = 1/5 Find P(X= 0) and P(X = 3).

Q: You are given a sample of two values, 5 and 9. Y ou estimate Var(X) using the estimator g(X1, X) =…

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Q: EX7.8) Let Y be a random variable having a uniform normal distribution such that Y~U (2,5) Find the…

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Q: (i) The mean of x (ii) P(x< 2).

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Q: Consider a random sample from NB(r, p) where the parameter r is known to be 3. An experiment is run…

A: Consider a random sample from  where the parameter r is known to be 3. An experiment is run with n =…

Q: If Var(X1) = 2, Var(X2) = 4, Var(X3) = 3, Cov(X1, X2) = 1, Cov(X1, X3) = -2, and X2 and X3 are…

A: Solution

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: If X is a poisson variate such that p ( x = 1 ) = 24 P ( x = 3 ). Find the probability p ( x = 0)o…

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Q: If X is a Poisson variate with mean , show that =1\| = ? 2 Е(x)- ЛЕ(x +1). If л%3D1 show that E\x -…

A: Poisson distribution:

Q: Given that P(X = 2) = 45P(X = 6) - 3P(X = 4) for a Poisson variate X. Find a. P(X > 1) b. P(X < 2)

A: First we have to determine the parameter of Poisson variable X with the help of given equation.

Q: If for a poisson variate 2p ( x = 0 ) = p ( x = 2 ). Find the probability that %3D i) p(x<3), i)…

A: It is given that 2Px=0=Px=2. The pmf of a Poisson distribution is PX=x=e-μμxx!.

Q: If the PDF of X is f(x)=2x/k2 for 0<x<k, for what value of k is the variance of X equal to 2?

A: The probability density function of Xf(x)=2x/k2      for 0&lt;x&lt;kfor what value of k the…

Q: Let X - T(28). Find P40(x) (50th percentile of X)

A: The (100p)th percentile is the value xp of the distribution such that (100p)% of the distribution…

Q: Let I be an indicator variable with p(I) = {p , I=1 } {1-p , I=0}. Show that the variance of I is…

A: The mean is calculated as follows: EI=∑I×PI=1×p+0×1-p=p

Q: Suppose f(x) = 0.20 for 0 <x < 5. Determine the mean and variance of X.

A: The objective is to find mean and variance

Q: Given f(x) = { (x2+1)/30; x = -2,-1,0,1,2  0; elsewhere ] Find the mean and variance of X.

A: X-2-1012f(x)

Q: (i) (ii) P(x s 2). The mean of x

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Q: Let X - T(25). Find P30(X) (30th percentile of X)

A: Solution: From the given information, X follows T distribution with degrees of freedom 25.

Q: Suppose the conditional mean function is Y = Bo + B1X + B2X² + B3X3 + U where E[U|X]3D0. By mistake,…

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Q: If X is a Poisson variate such that 4) + 90 P(X=6), find the P(X=2)=9P variance (X =

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Q: Show that (X+1)/(n+2) is a biased estimator of the binomial parameter θ. Is this estimator…

A: It is given that  X ~ Bin( n, θ ) We know that  E( X ) = nθ

Q: 1. Let X be an RV with PDF - f(x) = {1 = |x| a. Find the mean of g(x) = 5x² - 1. b. Find the…

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Q: 1 b) For any data set, approximately 95% of the observations fall in the interval (T − 2s, T+2s).…

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Q: Let X Poisson(A) and Y = vX. Use the delta method to approximate the mean and variance of Y.

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Q: Q. 25 If a Poisson variate X is such that P (x = 1) = P(x=2), Work out P (x = 4).

A: Given that X follows poisson distribution with parameter λ. Then the probability function of X is…

Q: Suppose X ~ N(2,3). What value of x has a z-score of -0.67?

A: Given, X ~ N(2,3) Implies, Mean = 2 Standard deviation = 3

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

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Q: If X is a random variable with pdf f(x) = 2x − 2 where x = (1, 2), find the variance of Y = 2X - 3.

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Q: The value of the correlation r = (x,y) for the information would be: n = 8, Sum(x) = 609, Sum(y) =…

A: Given: The values are as follow:                           n=8; ∑x=609,∑y=504;∑x2=47995; ∑y2=32954…

Q: fx(x) = 2e¯A* - 2x 1,2....,) %3D

A: Given, fxx=λe-λx Consider the given function as fx=λe-λx To find mean and variance

Q: Given pdf f (x) = 1.5x2  for −1< x < 1. Determine variance of X.

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Q: If u = x1x2 + x2X3 + X3X1, then find the relative percentage error in the computation of u at x1 =…

A: In the given question we have to calculate the relative percantage error in computation of u where…

Q: The variation of Y around its mean can be decomposed into which two parts?

A: Note: Hey there! Thank you for the question. As it is not mentioned whether Y is the response…