Given: X and Y have a normal distribution with mean_x = 19, var(x) = 5 mean_y = 11, var(y) = 1.
Find Probability that X + Y > 22
Find an x such that Probability that x<(X − Y)<10 =0.2
Given: X and Y have a normal distribution with mean_x = 19, var(x) = 5 mean_y...
Given: X and Y have a normal distribution with mean_x = 20, var(x) = 4, mean_y = 10, var(y) = 2. Find x such that Probability that x<(X − Y)<10 =0.2
X and Y have the bivariate normal distribution. You are given: E[X]=10 E[Y]=-5 E[XY]=-46 E[Y|X=2]=-77/9 E[X|Y=2]=17 Calculate Var[Y|X=x] + Var[X|Y=y] a) 6.5 b) 6.8 c) 7.00 d) 7.22 e) 7.43
Let X and Y have a bivariate normal distribution with parameters μX = 10, σ2 X = 9, μY = 15, σ2 Y = 16, and ρ = 0. Find (a) P(13.6 < Y < 17.2). (b) E(Y | x). (c) Var(Y | x). (d) P(13.6 < Y < 17.2 | X = 9.1). 4.5-8. Let X and Y have a bivariate normal distribution with parameters Ax-10, σ(-9, Ily-15, σǐ_ 16, and ρ O. Find (a) P(13.6< Y < 17.2)...
1. Suppose (x, Y) has bivariate normal distribution, E(x) E(Y)- 0, Var(X) σ , Var(Y) σ and Correl(X, Y) p. Calculate the conditional expectation E(X2|Y).
1. Two normal random variables X and Y are jointly distributed with Var(X) 25 and Var(Y) 1600. It is known that P(Y>80| X = 50) 0.1 and P(Y 22 X 40) 0.7886 (1) What is the correlation coefficient between X and Y? (2) What is the expected value of Y given X 50?
1. Suppose you have two random variables, X and Y with joint distribution given by the following tables So, for example, the probability that Y o,x - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),J(Y). (b) Find the conditional distribution (pmf) of Y give X, denoted f(YX). (c) Find the expected values of X and Y, EX), E(Y). (d) Find the variances of X and Y, Var(X),Var(Y). (e)...
х 1 4 5 4. The probability distribution of a random variable X is given below -4 3 P(X=x) 0.1 0.2 0.3 0.2 a) Find E(X) 0.2 b) Find Var(X)
Standard Normal Distribution Binomial Distribution 21 22 Area to the left of zi Area to the left of z2 Desired Area N p X p(x) To find: Area Between Area Between 1.. 20 0.3 0.2 -1.2 0. Task 1 Compute the values in the highlighted cells 6 60 9 10 11 12 13 14 15 16 17 18 19 20 E(x) = Var(x) Task 2 Compute values in the highlighted cells and draw pdf
5. Given below are the probability distribution of two assets-X and Y States of Economy Probability MEGA BOOM BOOM NORMAL BUST MEGA BUST 0.1 0.2 0.4 Expected returns of the 2 assets (%) - X Y 50 100 40 70 30 50 10 -20 -10 -50 0.2 0.1 Which one has higher stand-alone risk? (Compute Coefficient of Variation]
you have two random variables, X and Y with joint distribution given by the following table: Y=0 | .4 .2 4+.26. So, for example, the probability that Y 0, X - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),f(r). (b) Find the conditional distribution (pmf) of Y give X, denoted f(Y|X). (c) Find the expected values of X and Y, E(X), E(Y). (d) Find the variances of X...