1)
X/Y | 0 | 1 | P(X) |
0 | .15 | .25 | .15+.25=.40 |
1 | .45 | .15 | .60 |
P(Y) | .15+.45=.60 | .40 | 1(total) |
2)
=.15/.60
=.250
3)
=.25/.40
=.625
A joint probabilty mass table is given as follows: 0 0.15 0.25 1 0.45 0.15 1)...
Table 1 Joint PMF of X and Y in Example 5.1 x=01 X=1 | 1 Fig. 1 shows PXY()PXY( JointPMF ? 2 Fig. 1. Joint PMF of X and Y (Example 5.1). a. b. c. d. Find P(X-0,Y<1). Find the marginal PMFs of X and Y. Find P(Y-1X-0). Are X and Y independent?
5. (40 points) Let f(x,y) = (x + y),0 < 2,2 <y < 1 be the joint pdf of X and Y. (1) Find the marginal probability density functions fx(x) and fy(y). (2) Find the means hx and my. (3) Find P(X>01Y > 0.5). (4) Find the correlation coefficient p.
(f) Find the conditional pmf of X given Z. Identify this
conditional distribution as a distribution known in class, and
give
the explicit parameters for the known distribution.
(g) Find the conditional expectation of X given Z.
2. (Lec 13 &15 & 16 pairs of discrete R.V., conditional pmf and conditional moments, 17 pts) We are studying the flow of packets at a switch, which receives packets from two transmission paths, during a given period of time. Let X and...
1. The joint PDF of two random variables are given in the following table a) (0.3 points) Are X and Y independent? Explain. b) (0.3 point) Find E(X) c) (0.3 points) Find E(Y) d) (0.4 points) Find E(max(X, Y)) e) (0.4 points) Calculate P(X Y). ) (0.5 points) Calculate covariance of X and Y g) (0.5 points) Calculate correlation coefficient of X and Y 0 0.32 0.48 10.080.12
1) Suppose that three random variables, X, Y, and Z have a continuous joint probability density function f(x, y. z) elsewhere a) Determine the value of the constant b) Find the marginal joint p. d. fof X and Y, namely f(x, y) (3 Points) c) Using part b), compute the conditional probability of Z given X and Y. That is, find f (Z I x y) d) Using the result from part c), compute P(Z<0.5 x - 3 Points) 2...
1. Consider a discrete bivariate random variable (X,Y) with the joint pmf given by the table: Y X 1 2 4 1 0 0.1 0.05 2 0.2 0.05 0 4 0.1 0 0.05 8 0.3 0.15 0 Table 0.1: p(, y) a) Find marginal distributions of X and Y, p(x) and pay respectively. b) Find the covariance and the correlation between X and Y.
x P(x) 0 0.25 1 0.2 2 0.15 3 0.4 Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places
Let X and Y have the following joint distribution: X/Y -1 1 0 0.2 0.15 2 0.1 0.2 4 0.25 0.1 a) Find the probability distributions for X and Y b) Find E[X] and E[Y] c) Find the probability that X is larger than 1 d) Find E[XY]
1) Let random variables X and Y have the joint PMF: otherwise a) Calculate the value of c b) Specify the marginal PMFs Pr(x) and P- c) Calculate P[X +Y<0].
Two random variables have joint PDF of F(x, y) = 0 for x < 0 and y < 0 for 0 <x< 1 and 0 <y<1 1. for x > 1 and y> 1 a) Find the joint and marginal pdfs. b) Use F(x, y) and find P(X<0.75, Y> 0.25), P(X<0.75, Y = 0.25), P(X<0.25)