a. Verify that f(x, y)is a joint density function. Find the P[(X, Y) EA] where 4 = {(x, y) | < x < 0
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Q: Let (X,Y) have the joint density function f(x,y) = { (6/5)(1+x+y) for 0 < x, y < 1, x+y<1 otherwise…
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- Let and Y have the joint density function 2, 0= cx for -x < y< x, 0 < x < 1, and Assuming that X and Y have joint distribution f(x, y) f(x, y) = 0 otherwise. Find the density of W = X – YPlease show all stepsLet Y₁ and Y₂ have joint density f(y₁, y2) = 3c(1 - y₂) on 0 ≤ y ≤ 2 and 0 ≤ y₂ ≤ 1. What is the value of c? In question In question A: B:2 C: D:3 above, what is the value of P(Y₂ 1)? A: 0.55 B: 0.1 C: D 113If we want to estimate sales based on the test scores, which variable is the dependent variable and which is the independent variable? Justify.If the joint density function of X and Y is given f(x, y) = {k(x + 2y), 0 < x < 1; 1 < y< 2 0, elsewhere <(x - a. Evaluate the value k. b. Estimate P(X+Y < 2). C. Find the marginal distribution of X and the marginal distribution of Y.Q3 The joint density function of X and Y is given by: Find: 1- P(X> 1nY0,y>0 otherwise fxy(x, y) = {Ce STRIJHelp me fast with detail explanation. Definitely I will give Upvote.4. Consider the density function f(x) = SkVx, 0.54. Suppose that the joint distribution of X and Y can be modeled by the following probability density function: S(x, y) = 6x³y, [0, 0a) Find the conditional density of X, given Y = y, and that of Y , given X = x. Make sure to define the support of each density function. b) Find the density function of Z = XY . Make sure to define the support of f (z).2. Let the bivariate continuous random vector (X,Y) have the following joint probability density function: {; c 0SEE MORE QUESTIONSRecommended 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