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Q: 2. The continuous random variables X and Y have known joint probability density function f(x,y)…
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Q: Q 6.2. Let X = (X₁, X2, X3)T~ MVN(ux, Ex) where -3 (1) μχ = Compute the distribution of Y and Σχ -…
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- Let X and Y are two random variables with p.d.f as F(x,y) = 3x^2y+3xy^2,0 < x< 1,0 < y < 1. (i) Find conditional density of X given Y. (ii) Find the mean, mode and standard deviation of r.v Y. (iii) Correlation between X and Y. (iv) Check that X and Y are independent or not?2. Let X be a random variable with density function ) = √(2x² - + f(x) = Find the expected value of g(x) = 2X+1. 8x2 +5x + 6), 1 < x < 2, 0, elsewhereIf X is a continuous random variable find the CDF and density of the function y = x/3
- Suppose that two continuous random variables X and Y have joint probability density function fxy = 1sxs2,0sy<3 elsewhere Find the strength of the relationship and interpret the findings.Be X a random variable with density function defined by f(x) = -2², , x>0. 3 Get the moment-generating function and based on it, calculate the average and variance of X.Normal distribution. The moment generating function of a random variable U is M(t) = (1 - 8t)^-7. Find: i)Probability density function, ii)Mean, iii)Variance of U.
- Let X,Y be two random variables with joint probability density function f(x, y) =0< Xe) The density function of a certain random variable X is given by xa-'(1– x)®-1 f(x) = {B(a,0) 0, if 0 0. i) Derive the expected value of X. ii) Derive the variance of X.The probability density of the random variable Z isgiven by f(z) = kze−z2for z > 00 for z F 0Find k and draw the graph of this probability density.
