Assume that random variables X and Y are independent, X has a discrete distribution such that P{X = 0} = P{X = 2} = while Y 2y, 0 < y < 1 has a density function f(y) = l0. otherwise %3D (1) Find P{Y
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- Suppose that X and Y are random variables with the joint density function cx? 0 2).Let X be a continuous random variable with density function be-bx for a > 0 f (x) = otherwise where b > 0. - find M(t) the moment generating function of X, then what is E(x) ?There are two components in an electronic system. Let X and Y denote the lengths of life in years. The joint density function of these variables f(x, y) = {ye-&+x) ,x 2 0, y Determine P(x>3) What is the probability that both components will exceed 3 years?
- Suppose that X and Y are random variables with the joint density function cx² + cy, 0 sx< 3,1The continuous random variables X and Y are statistically independent and have marginal density functions fx(x) = 2x, 0 1. y2' Calculate the probability P(X < 0.5, Y < 2)Consider two continuous random variables X and Y with marginal distributions g(x) and h(y)respectively and the joint density function given by: x > 0, 0 < y < 2 elsewhere. f (r.y) Then: X and Y ar statistically dependent f(x,y)#g(x)h(y) None of these f(ylx)=g(x)4. Let X and Y be independent, continuous random variables with densities and fx(x) = = fy (y) = = 0 {} if 0 < x < 2 otherwise. y if 0If the joint density function of X and Y is f(x, y) = 6e-2xe- -3y 0 < x <∞, 0 < y < ∞ and is equal to 0 outside this region, are the random variables independent?Find the density of U = Y1 +Y2, where Y1 and Y2 are independent random variables with densities (yı – 1), 3 < Yı < 4, (y2 + 2), 0 < Y2 < 1, fy, (y1) : fy,(y2) = otherwise, otherwise.Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON