Given
f(x,y) = (x+y) / 30
a)
P(X>=2,Y=1) = P(x=2,y=1) + P(x=3,y=1)
= 3/30 + 4/30
= 7/30
b)
P(X>2,Y<=1) = P(3,0) + P(3,1) = 3/30 + 4/30 = 7/30
c)
P(X+Y=4) = P(2,2) + P(3,1) = 4/30 + 4/30 = 8/30 = 4/15
d)
P(X=2|Y=1) = P(2,1) / P(Y=1)
P(Y=1) = P(0,1)+P(1,1) + P(2,1) + P(3,1) = 1/30 + 2/30+ 3/30 + 4/30 = 10/30
P(X=2|Y=1) = (3/30) / (10/30) = 3/10
If the joint probability distribution of X and Y is given by 30 for a-0,1,2,3y-0,1,2 Com pute fol...
If the joint probability distribution of X and Yis given by: fxy)-2xty48,for all x-0,1,2,3 and y-0,1,2 Determine Part a: P(Xs3,Y-1) Part b: P(X+Y-4) Part c: Part d: E(XY)]
Q(2) The joint probability distribution of X and Y is given by (2x-y)2 for x = 0, 1, 2 and y = 1,2,3 (Marks: 6,2,4) 30 f(x, y) = Find : (1) the joint probability distribution of U = 3X + Y and V = X - 2Y (11) the marginal distribution of U. (III) E (V)
1. If the joint probability distribution of X and Y is given by f(x, y) for = 1,2,3; y=0,1,2,3 · 42 2. Referring to Exercise 1, find (a) the marginal distribution of X; (b) the marginal distribution of Y. 3. Referring to Exercises 1 and 2, find (a) The expected value of XY. (b) The expected value of X. (c) The expected value of Y (d) The covariance of X and Y (COV(X, Y)). Round your final answer to 3...
Let X and Y have joint probability mass function fX,Y (x, y) = (x + y)/30 for x = 0, 1, 2, 3 and y = 0,1,2. Find: (a) Pr{X ≤ 2, Y = 1}(b) Pr{X > 2, Y ≤ 1} (c) Pr{X +Y = 4}. (d) Pr{X > Y }. (e) the marginal probability mass function of Y , and (f) E[XY].
I need help proving equation 1.2: All joint probability statements about X and Y can, in theory, be answered in terms of their joint distribution function. For instance, suppose we wanted to com- pute the joint probability that X is greater than a and Y is greater than b. This could be done as follows: P{X > a, Y > b} = 1 - P({X > a, Y > b}) 1 - P({X > a}C U {Y > b}) =1...
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...
Let X and Y be random variables, each taking values in the set {0,1,2}, with joint distribution P[X = 0,Y = 0) = 1/3 P[x = 0, = 1] = 0 P[X = 0, Y = 2] = 1/3 P[X = 1, Y =0] = 0 P X = 1, Y = 1] = 1/9 P[X = 1, Y = 2] = 0 P[X = 2, Y =0] = 1/9 P[X = 2, Y = 1] = 1/9 P[X =...
2. Given the random variables x and y with joint probability distribution X/Y - 4 2 -8 60 10.5 0.01 10.0 0.51 Show that EYx) * E%) E(X)
4. The joint distribution of X and Y is given by 0 otherwise (a) Are X and Y independent? Explairn. (b) Find the marginal probability function (pdf) of Y, fy (). (c) Provide the integral for finding P(X < Y), but DO NOT evaluate.
7. Let X and Y have joint probability mass function fx,y(x,y) = (z+y)/30 for x = 0, 1, 2, 3 and y-0,1,2. Find (a) Pr(X 2, Y=1} (b) PríX > 2, Y 1) (c) PrXY-4) (d) PrX>Y. (e) the marginal probability mass function of Y, and (f) E[XY]