P(X = Y +1)
note that there are N^2 tuples of (x,y)
in this number of cases with
x = y+1
are N-1
hence
required probability
= (N - 1)/N^2
)Consider a 아 which take on values on tix A-C,2 N)、N hare N-5c ha Joint distribution...
Consider a pair of random variables X and Y, each of which take on values on the set A (1.2,3,4,5). The joint distribution of X and Y is a constant: Pxyx,y)-1/25 for all(x.y) pairs coming from the set A above. Let the random variable Z be given as the minimum of X and Y. Find the probability that Z is equal to 5.
The discrete random variables X and Y take integer values with joint probability distribution given by f (x,y) = a(y−x+1) 0 ≤ x ≤ y ≤ 2 or =0 otherwise, where a is a constant. 1 Tabulate the distribution and show that a = 0.1. 2 Find the marginal distributions of X and Y. 3 Calculate Cov(X,Y). 4 State, giving a reason, whether X and Y are independent. 5 Calculate E(Y|X = 1).
2. Suppose that X and Y have a discrete joint distribution for which the joint p.f. is defined as follows: cly - xfor x = -3,-1,1, 2; y = -2, -1,0,1 Por f(x,y) = 1 0 0.w. x Determine the value of the constant c. Compute P(X<Y).
2) The random variables X and Y have the following joint distribution. 3 .25 2 .2 1.16 1.04 .05 1.04 1.01 .05 a) Find the correlation between X and Y. b) Provide intuitive reasoning for your result from part a). 3) Take the joint distribution of X and Y from the previous exercise, and consider L, and L, to be lottery tickets that pay according to the following scheme: Li = X if X <2, L, = 5 otherwise. L=L+Y...
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and 0 Y 3 2. Suppose also that the joint cumulative distribution function (cdf) of X and Y, for 0 < 2 and 03 y 3 2, is as follows: Fy). 16 [5] (a) Determine the marginal cdf Fx(x) of X and the marginal cdf Fy () of Y [5] (b) Determine the joint probability density function (pdf) f(x, y)...
Please give detailed steps. Thank you. 2. Consider the following joint distribution of two discrete variables X and Y: fx,y(x, y) 01 2 3 お88 Recall that the marginal distribution of X is defined as: fx(x) and the marginal distribution of Y is defined as fy(v) -xf(i) Find fx(x) and fy(y) in the support of X and Y (or in simpler terms, find 1), P(Y = 0), P(Y-1), P(Y-2) and P(Y P(X-0), P(X 3)) b. The conditional density of Y...
Consider the random variable X which can take on three values a − b, a, and a + b for real numbers a and b with b > 0. Moreover, P{X =a−b}=P{X =a+b} and P{X =a−b}=2P{X =a}. (a) Find the variance of X. (b) Find the cumulative distribution function of X.
Consider the following joint probability distribution on the random variables X and Y given in matrix form by Pxy P11 P12 P13 PXY-IP21 p22 p23 P31 P32 P33 P41 P42 P43 HereP(i, j) P(X = z n Y-J)-Pu represents the probability that X-1 and Y = j So for example, in the previous problem, X and Y represented the random variables for the color ([Black, Red]) and utensil type (Pencil,Pe pblackpen P(X = Black Y = Pen) = P(Black n...
3. Consider the joint probability distribution for Y and X. X/Y 2 4 6 1 0.2 0.21 2 10 201 3 5.2 0 2 a) Calculate the marginal densities for both Y and X. b) Show using the conditional distribution for Y and the marginal distribution for Y, that X and Y are not independent. c) Calculate the E(Y|x = 1)and V(Y | x = 1).