The discrete random variable X has probability mass function kx x = 2,3 2kx P(X = x) = x-1' x = 4,5 0,otherwise. Find the variance of X.

Q: Let X and Y be independent random variables, each with mean=mu and variance=sigma^2. Find the…

A: From the given information, Consider, X and Y be independent random variables,…

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: Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)

A:

Q: If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean…

A: Solution: From the given information, the probability density function of X is

Q: Suppose that f (x) = e* for 0 < x Determine the mean and variance of the random variable.

A:

Q: -generating function is as follows f(x)= 2x-1/16 , x=1,2,3,4 my answer is mean = 25/8, var = 170/16…

A: x 1 2 3 4 f(x) = 2x-116

Q: If X ~B(190,0.34), find mean and variance of x. (Rounded in 3dp.)

A: X ~B(190,0.34) Given a Binomial Distribution X ~B(n,p) Here, n = 190 , p = 0.34

Q: Let x be a continuous random variable with PDF 3 x > 1 x4 fx (x) otherwise Find the mean and…

A: Given PDF is fX(x) = 3x4,x ≥ 10,otherwise

Q: let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance…

A:

Q: Find the variance of the random variable X with a PDF given by 3x2 S* if - 1< x< 1, f(x) = 2…

A:

Q: Find the probability distribution of the random variable y, which represents the number of times…

A: Given, Y 1 2 3 f(y) 130 430 930

Q: Show that the conditional variance can be written as σ^2 (X) = E { Y^2 | X} −(E[Y | X])^2     no…

A: A variance is a measurement of how far each individual in the dataset is residing from the mean and…

Q: A random variable Y has a uniform distribution over the interval (8,, e,). Derive the variance of Y.…

A:

Q: If the variance of a continuous random variable X with pdf f(x) is noted as V(X), what is its…

A: Given: X had pdf f(x) and Variance of random variable X is - V(X)

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 =…

A: A random variable follows a Normal distribution with mean μ and variance σ2 Random Variable Mean…

Q: how that the variance of a geometric random variable X; is given by V ar(X) = q/p^2 .

A:

Q: Y, = XB + ɛ, Show that the model variance in model Yi unbiased estimator of

A:

Q: Suppose X is random variable with E(X^2)= 10 and E(X)=2. What is the variance of X? Suppose X is a…

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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)

A:

Q: Let Y be a random variable with pdf f(y)= (1/18)(y^3−1) for 1 2.5). (b) Calculate the variance of Y…

A: Solution

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

A:

Q: Determine the mean and the variance of X.

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

Q: Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.

A: Given, Now,

Q: Q3/A/ Let X be a r.v with p.d.f f(x) = e-ll - co <x<0, then the value of variance of X is -

A: Given : X is a random variable with PDF             fx=12e-x , -∞&lt;x&lt;∞ To find : Variance of X

Q: 2x A random variable X has the density function f(x)= } k- 0, Otherwise. For what value of k the…

A: The given probability density function is as follows: The variance of X is equal to 2.

Q: True or False: For an exponentially distributed random variable, x, P(x) = 1/(b - a).

A: It is given that the statement about to the exponential distribution. Here, need to find out the…

Q: Let X and Y be two random variables with joint probability mass function: p(x,y)=xy(1+y) for X=1,2,3…

A: Given that X and Y are two random variables…

Q: Let X and Y have the joint pdf f(x,y)= x+y , 0<=x<=1, 0<=y<=1.  Calculate the mean(x)

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: calculate the variance of g(X) =X^2+2, where X is the random variable with probability distribution…

A: calculate the variance of g(X) =X^2+2, where X is the random variable with probability distribution…

Q: let X and Y be independent standard normal random variables. Determine the pdf of W = X^2 + Y^2.…

A: Result: If X~N(0,1) then X2~χ2(1) χ2(n1)+χ2(n2)=χ2(n1+n2)  E(χ2(n))=n and V(χ2(n))=2n

Q: Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is

A: From the given information, the joint density function for X  and Y is,

Q: Let Y be a random variable with the mgf M(t) = .35e^(−4t) + .1 + .25e^(2t) + .3e^(4t). (a) What is…

A: Given information: Mt=0.35e-4t+0.1+0.25e2t+0.3e4t      =0.35e-4t+0.1e0t+0.25e2t+0.3e4t a) The pmf of…