If the joint probability density function of two continuous random variables X and Y is given by f(x; y) = 2, 0 < y < 3x, 0 < x < 1; find (a) f(yjx), (b) E(Y jx), (c) Var(Y jx).
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If the joint
given by
f(x; y) = 2, 0 < y < 3x, 0 < x < 1;
find
(a) f(yjx),
(b) E(Y jx),
(c) Var(Y jx).
Step by step
Solved in 3 steps with 2 images
- Example 10 : If X is a continuous random variable and Y = aX + b, prove that E(Y) = a E(X) + b and V(Y) = a².V(X), where V stands for variance and a, b are constants.Let 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 7/20If F(x) is cumulative distrbution function of a continuous random variable X, the probability (function f(x) is the dervative of F(x (Fa)se (Trụe
- 3) Find the mean and variance of the random variable X with probability function or density f(x). (a)f(x)={k(1-x), –15xs1 O otherwise (b) ƒ(x) = k/3× , x = 1,2,3,... Note: in this problem, you need to first find the values of k.2. If the random variable X has the probability density function f(x) = (1-x²), -1 < x < 1, 3 4 what is the variance of 15X + 2?The joint probability function of two discrete random variables X and X is given by f(x, y) = cxy for x = 1, 2, 3 and y = 1, 2, 3, and equals zero otherwise. Find (a) the constant c, (b) PCX = 2, Y = 3), (c) P(1 ≤X ≤ 2, Y ≤ 2), (d) P(X22), (e) P(Y ). (c) P ¹). (c) P ( < X < ³), (d) P(Y < ¹), (e) whether X and Y are independent. dix dy C CX
- If the joint probability distribution of X1 and X2 isgiven by f(x1, x2) = x1x236for x1 = 1, 2, 3 and x2 = 1, 2, 3, find(a) the probability distribution of X1X2;(b) the probability distribution of X1/X2.The probability density function of a discrete random variable X is given by the following table: Px(X = 0) = .073 Px(X = 1) = .117 %3D Px(X = 2) = .258 Px(X = 3) = .322 Px(X = 4) = .230 %3D i) Compute E(X). ii) Compute Var(X).If X is a random variable with probability density function 32 f(x) = A* for x = 0, 1, 2, 3, 4 and 5, the var(X)