The random variables X and Y have joint density function dive³, x>0₁y>0 0, otherwise (1) Compute the marginal density function of Y, (2) Compute P(X>1|Y=y), (3) E[X]Y=y]. 7₁ f(x,y) = y
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- A random variable X has a density function (cx² f (x) = {cx 1 2) P(1/2A random variable Y have a distribution with parameter a > 0 and y, > 0 if its density function is given by: (ay“ if y> yo fV) = ya+T (0, elsewhere i) Derive the mean of Y. Show all necessary steps. ay (a-2)(a-1)²' ii) Show whether or not that the variance of Y is ·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 0Let X and Y be continuous random variables with joint p.d. f. f(x,y) = {* (12x for 0< y< 2x < 1 elsewhere The conditional density function of Y given X = x isPlease Answer Asap4) The joint density function of the random variables X and Y is given by (&xy f(x, y) = 0SXS1,0 sysx otherwise Find (a) the marginal density of X, (b) the marginal density of Y, (c) the conditional density of X, (d) the conditional density of Y.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