etermine the marginal density function of X.
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etermine the marginal density
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- Suppose that Y is a continuous random variable. Show EY yfr(y)dy.Let X and Y be jointly continuous random variables with joint PDF cx +1, 2,y> 0, x+ y<1 0, fx,x (x, y) = otherwise. Then the constant c= And the probability that P(Y < 2X²) = ;: Here a = and b =Let Y be a continuous random variable. Let c be a constant. PROVE Var (Y) = E (Y2) - E (Y)2
- Let the random variables x and y have joint pdf as follows: f(x,y) = (11x² + 4y²), 0Let X and Y be a pair of continuous random variables with a joint density fx,y(x,y). Assume that fx,y(x,y) = cxy for x greater than or equal to 0, y greater than or equal to 0, and x + y less than or equal to 1. Here c is a constant. Assume that fx,y(x,y) is 0 elsewhere. What is the constant c equal to? With the value of c, what is E[XY]?Let X and Y be continuous random variables with joint distribution function, F (x,y). Let g (X,Y) and h (X,Y) be functions of X and Y. PROVE Cov (X,Y) = E[XY] - E[X] E[Y]Let X be a (continuous) uniform random variable on the interval [0,1] and Y be an exponential random variable with parameter lambda. Let X and Y be independent. What is the PDF of Z = X + Y.Suppose that the random variables X and Y have the following joint probability density function. f(x, y) = ce 3x - 9y 0 < y < x. = Find P(X < 2, Y <).X and Y are independent random variables with the same uniform density o n [2, 3, 4, 5, 6]. Find P{X = Y} and P{X > Y}