then what is the marginal density function of X, where nonzero?
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![27. If the joint density of the random variables X and Y is
[emin{x,y) - 1] e-(x+y)
if 0 < x, y <∞
f(x, y) =
0
otherwise,
then what is the marginal density function of X, where nonzero?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8020c2ff-a953-4183-8fd3-32b86da8a816%2Fe99a8bf5-1f4f-4e13-aa7f-c4509235219e%2F2xjjrya_processed.png&w=3840&q=75)
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- The density function of two random variables X and Y is fxy (x, y) = 16 e-4 (x+y). u (x) u (y) Find the mean of the function (X, ¥)= 5 for 0 < X s; 1 = -1 for < X and lor< Y 2 = 0 for all other X and Y4) 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.4) The joint density function of the random variables X and Y is given by S8xy 0 s xs 1,0 s ys x f(x, y) = 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.
- 3. Let X be a continuous random variable. Let f(x) = c(x − 1)³ and Sx = [1,3]. Hint: (x - 1)³ = x³ + 3x − 3x² - 1 (a) What value of c will make f(x) a valid density? (b) What is P(X = 2)? (c) Find E(X). (d) What is P(1 < X < 2)?AsapLet Y1 and Y2 be two jointly continuous random variables with joint probability density function f (y1, Y2) = {10 y Y1 , 0 < y1 < y2 < 1, and 0 elsewhere. The marginal probability densities function of Y1 is fi (y1) = 5 yf, 0 < y1 <10 10 fi (y1) = y1 (1 – yf), 0Let Xand Y be two continuous random variables with joint probability density [3x function given by: f(x.y)%D 0sysxsl elsewhere with E(X) = ECX)- EC) - EC*)= ;and E(XY) = 10 3 E(Y*) = - and E(XY) =; %3D Then the value of the variance of 2X+Y is: O 3/80 O 91/320 43/320 7/20The random variable Y has probability density function f(V) = k(y + y³), 0 2. Hence find PG < Y <). iii) Find the variance of Y.The density function of two random variables X and Y is ,-2(x+y) fx,r (x, y) =u(x)u(y)4e¯¾x*y) X,Y Find the mean value of the function e-*+),Let X and Y be independent normally distributed random variables with mean zero and variances og = 1 and of = 4. (a) Write the joint probability density function fx.y (r, y). • (b) Define new random variables U = aX + Y and V = X – Y, where a + -1 is a real number. Find the absolute value of the Jacobian of transform from X, Y to U, V. (c) Find the joint probability density function for U and V. Find a for which U and V are independent random variables. Write down fu,v (u, v) for this a in the answer.1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.Let X and Y be two continuous random variables with joint probability density [3x function given by: f(x,y)= 0SEE MORE QUESTIONSRecommended textbooks for youLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning