Let X1, X2, andX3 be independent and normally distributed random variables with E(X1) = 4, E(X2) = 3, E(X3) 2, Var(X1) = 1, Var(X2) = 5, Var(X3) = 2. Let Y = 2X1+ X2 – 3X3. Find %3D the distribution of Y.

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: 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: Calculate value of (t) if: first sample mean = 85, second sample mean = 91, and o x1-x2 =

A: We want to findvalue of t

Q: X is a discrete uniform (1,3) random variable. When X=x, Y is discrete uniform (1,x). (a) Find…

A: We are given here that:P(X = 1) = P(X = 2) = P(X = 3) = 1/3 as X is a discrete uniform distribution…

Q: Let X and Y be identically distributed with mean 3 and variance 25. (a) If X and Y are uncorrelated,…

A: Let X and Y be identically distributed with mean 3 and variance 25 . Therefore, EX=3,  EY=3, VarX=25…

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: The regression lines between two random variables X and Y is given by 3X + Y = 10 and3X + 4Y = 12…

A:

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: Suppose the variance of the difference of two random variables X and Y is zero. Then, show that X =…

A: A random variable is a function that associates a real number with each element in the sample space.…

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

A:

Q: Let X and Y be identically distributed with mean 4 and variance 25.(a) If X and Y are uncorrelated,…

A: a) If X and Y are uncorrelated then Cov(X,Y)=0, given V(X)=V(Y)=25 Answer(a): 50

Q: Explain why y is considered the least squares estimator of the mean of Y, µy.

A:

Q: Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a no random variable…

A: Given that X1 follows Normal distribution with E(X1)=2 and V(X1)=3. X2 follows normal distribution…

Q: The profit for a new product is given by Z = 3X-Y -5. X and Y are independent random variables with…

A: Given: Var(X) = 1  Var(Y) =2 X and Y are independent. Z = 3X-Y-5

Q: b) Find the variance Var(X) of X.

A:

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: Consider (Y, X) values in a population as (8, 2), (9, 3), (10, 3), (12, 5), (14, 6), (16, 6) and…

A:

Q: Suppose X and Y are two random variables with covariance Cov(X, Y) = 3 and Var(X) = 16. Find the…

A: The correlation coefficient between two random variables X and Y is defined as:  ρ(X, Y) = Cov(X, Y)…

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

A: Given Data: Var(X)=8 Var(Y)=6

Q: Two regression lines of a sample are X+6 Y=6 and 3X+2Y=0. Find the correlation coefficient.

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Q: Let X be a random variable distributed as a Normal with mean 0 and variance 2 (i.e., X ~ N(0, 2)).…

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Q: the random variable Y is such that : E(2Y+3)=6    and    Var(2-3Y)=11 find      E(Y^2)

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Q: A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1). Find…

A:

Q: In the 2012 presidential election, exit polls from the critical state of Ohio provided the following…

A: As per our guidelines, we are allowed to answer first question only. Thanks   Given Data :

Q: Find variance of Y1

A:

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

A:

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: Determine the mean and the variance of X.

A: Given that  f(x) = 0.125 x    for 0<x<4   We know that  Mean = E(x) = ∫x.f(x) dx variance V(x)…

Q: Find the new data point (x,y) in which x=2 from the data points (1,3) and (4,12)

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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…