b. Find E[X(X – 1)] for Poisson random variable. Use the result to find the variance of X.

Q: Let X be a random variable with mean E[X] = 20 and variance Var(X)= 3. Define Y = 3 - 6X. Calculate…

A: We have given that, Let X be a random variable with mean E[X] = 20 and variance Var[X] = 3   We know…

Q: Compute the mean and variance for the linear function W = 2X - 4Y.

A: It is given that For X, mean = 1.3, Variance = 0.21 For Y, mean = 0.3, Variance = 0.21 Cov(X, Y) =…

Q: A random variable Y has a uniform distribution over the interval (?1, ?2). Derive the variance of Y.…

A:

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

A:

Q: Let X and Y be independent random variables with means ux, μy and variances o, oy. Find an…

A: Given:  Random variable x and y are independent with means ux, uy  , varience σ2(x) and σ2(y)  E(x)=…

Q: Clearly describe the advantages of portfolio diversification. Suppose, the rates of return on two…

A: Portfolio Diversification        Portfolio Diversification is the process of investing your money in…

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: Let X and Y be independent random variables distributed as N(-1, 1) and N(1, 1), respectively. Find…

A: X follows a  normal distribution with , µ= -1 , σ= 1. Y follows a  normal distribution with , µ= 1 ,…

Q: Find the variance with solution

A:

Q: Let X is continuous uniform (1,7) and Y is exponential with mean 2. If the correlation coefficient…

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Q: Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type…

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Q: Let X have a mean of 132 and a variance of 32. Define Y=X² + 2X+1. Compute the (a) mean and (b)…

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Q: The random variable Y has the Poisson distribution with a mean of 50. (a) What is the variance of Y?…

A: Let Y have a Poisson distribution with a mean of 50.The PMF of Poisson distribution with a mean of…

Q: Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type…

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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: Discrete random variable Y has the CDF FY(y) as shown below. Find the variance of the random v

A: From the given plot,The pdf of Y is

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: A random variable X is normally distributed with a mean of 100 and a variance of 500, and a random…

A: Given,E(x)=100V(x)=500E(y)=200V(y)=400r=-0.5

Q: Let X; be independent Uniform(-10,10) random variables, for i=1, 2, ..., 5. Let Y = X₁+X₂+...+X5.…

A: Let  be independent random variable follows uniform(-10, 10) distribution for i=1, 2,....., 5the…

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

A:

Q: continuous random variables Z is known to have an Erlang (2,1.3) type PDF. what is the variance of Z

A: Given that Z is a continuous random variable having a distribution Erlang with parameters (…

Q: Let X and Y be nonnegative integer-valued discrete random variables such that JC. 2-m-n P(X = m, Y =…

A: Given the joint pmf of the nonnegative integer-valued discrete random variables X and Y:

Q: If a random variable X has the moment generating function Mx (t) = 2 - ť Datermine the variance of…

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Q: Let X∼Uniform(0,1) distribution. Find the PDF of Y= 3√X and derive the expected value and the…

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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: Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the…

A: The given pdf is shown below:

Q: In a poisson distribution P(X=0)=P(X=2).Find the variance V(X) of X.

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Q: The random variable X takes value O with probability, and value 1 with the remaining probability.…

A: We have given information, The random variable X takes value 0 with probability 13, and 1 with…

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

A:

Q: f(X)= 3/8( 4x - 2x2 )         0<* x <* 2     (* less or equal to) a.  Find the variance of X.

A:

Q: Let X be a random variable and Y = aX + b with a ̸= 0. Show that the correlation between X and Y is…

A: Given data: Let X be a random variable and Y = aX + b with a ≠ 0. To show: Show that the correlation…