Show that any random variable, X, is uncorrelated with a constant show Cov(X, a) = 0. а.
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Q: If the random variables X and Y are orthogonal, then their correlation is zero. Rxy =0
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Q: Is cov(X, Y) random?
A: Given :Is cov(X, Y) random?
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Q: 5. Show that given random variables X and Y, Cov(X, E(Y | X)) = Cov(X, Y).
A: For the random variable X and Y, we need to show that: Cov[X, E(Y|X)] = Cov(X,Y)
Q: • The pdf of a uniform random variable is given by: Ax) = -0,xb • Find the CDF.
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Q: Let X and Y be random variables having the same distribution. Show that Cov(X +Y, X – Y) = 0. |
A: Given that X and Y are same distribution thenE(X2)=E(Y2) , E(X)=E(Y) Show that Cov(X+Y,X-Y)=0
Q: Let Y be a discrete random variable. Let c be a constant. PROVE Var (Y) = E (Y2) - E (Y)2
A: We have to deduce the formula of variance.
Q: .. Let X, Y, Z be random variables each having a mean µ and variance o². rurther, let Cov(X, Y) = 2,…
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- Let X be a Gaussian random variable (0,1). Let M = ln(5*X) be a derived random variable. What is E[M]?Find the variance by calculating the first two moments of the random variable X = (- 1 / λ) ln (1-U), where U ~ U (0,1) and λ> 0.X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2
- If X is a random variable having the standard normaldistribution and Y = X2, show that cov(X, Y) = 0 eventhough X and Y are evidently not independent.We have a random variable X and Y that have the joint pdf f(x) = {1 0<x<1, 0<y<1} {0 otherwise} If U = Y-X2 , what would the pdf of the random variable U be? What is the support for the random variable U? Would there be any critical points? (use CDF technique)Consider random variables X and Y with the joint PDF below find pxy