Homework Answers
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
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)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...
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...
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....
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...
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...
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...
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...
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...
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...
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).
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.
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 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).
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