X and Y are discrete random variables with a joint density function as follow f(x, y) = 1) = {²+ ( x² + y) 0, (x² + y) x = 0,1,2; y = 0,1,2 Otherwise 1) Find the value of Cov[X, Y] 2) Find the value for both E(Y|X = 1) and E(X|Y = 2)
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![X and Y are discrete random variables with a joint density function as follow
{ 2 1 (x² + y)
24
0,
f(x, y) =
1)
2)
(x² + y) x = 0,1,2; y = 0,1,2
Otherwise
Find the value of Cov[X, Y]
Find the value for both E(Y|X = 1) and E(X|Y = 2)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21bccc94-88a4-4d53-b62c-c918d6bcc9f0%2F66dada35-c47a-4ccf-9fa2-89b6cac5c57a%2F28jxkbw_processed.jpeg&w=3840&q=75)
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- b) Suppose that the joint density function of random variables X₁ and X₂ is given by f(x₁, x₂)= = 0, 0< x₁ < x₂ <2 otherwise i) Draw a sketch of the area where f(x₁, x₂) is not zero. ii) Find P(X₂ < 1). iii) Find E(X₁X₂).b) Let Z₁-N(0,1), and W₁ = Y~N(0,1), for i=1,2,3,...,10, then: dx dy i) State, with parameter(s), the probability distribution of the statistic, T = - 154 ii) Find the mean and variance of the statistic T = ₁² 10 iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. iv) Find the value of ß such that P(T> B) = 0.01, where T = ₁2₁² +².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-*+),
- Q1) Discrete joint variables X and Y with probability density f(x,y) (pdf) are given in this table. Find: 1) The Covariance Cov(X,Y)? (Cov(X,Y) = MxY-MxMY) 2) The correlation (pxy) between X and Y where Pxy = Cov(X,Y) PXPY Y 3 fx(x) f(x,y) 1 2 1 1/4 1/4 0 X 2 0 1/4 1/4 fy(y) Note that 2 n=2 n=3 Px² = Σn²±²x² f(x, y) - μ and py² = Σ3y² f(x, y) – µ Zk=0• Find the density of Z = (X+ Y)2, where X and Y are independent uniform random variables over (-1, +1).6) The random variables X and Y have joint density f( x, y) = x2-y2 for 1< x, 1s y and f( x, y) = 0 otherwise. %3! Compute the joint density of U = X /Y and V = X Y.
- 2. Let X and Y be jointly continuous random variables with joint PDF x + cy2 0, OSXS1,0Let X and Y be random variables with joint density function, f(x, y) = e-, 0. If Z = X + 2Y and W = X. Which of the following is true? (A). The joint PDF of W and Z is e-w, and W and Z are independent (B.) The joint PDF of W and Z is e-w, and W and Z are independent (C) The joint PDF of W and Z is te-", and W and Z are dependent (D.) The joint PDF of W and Z is e-w, and W and Z are dependent В O A ос2. Let X and Y be jointly continuous random variables with joint PDF x + cy2 0, OSXS1,0Sys1 elsewhere a) Find the constant c Find the marginal PDF's fy(x) and fy(y) c) Find P(OSXS1/2,0SYS1/2) b)Let X and Y be continuous random variables having a joint pdf given by f(x, y) = e-*, 0sysx 3).1) The joint probability density function of the X and y random variables, fx,y (xiy)= cx,0Let X and Y be independent random variables. X is N(1,9) and Y is uniform on the interval {--1, 1]. Lat Write down the joint density for (X,Y) o Give the mean and variance of Y c) Give the median of X I dY Give the correlation coefficient p of X and YSEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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