SOLUTION: (4 points) The joint probability mass function of X and Y is given by p(1,1)=0.45 p(2,1)=0.05 p(3,1)=0.1 p(1,2)=0.05 p(2,2)=0 p(3,2)=0.05 p(1,3)=0.1 p(2,3)=0.1 p(3,3)=0.1

Question 1188501: (4 points) The joint probability mass function of X and Y is given by
p(1,1)=0.45 p(2,1)=0.05 p(3,1)=0.1
p(1,2)=0.05 p(2,2)=0 p(3,2)=0.05
p(1,3)=0.1 p(2,3)=0.1 p(3,3)=0.1
(a) Compute the conditional mass function of Y given X=1: P(Y=1|X=1)=
P(Y=2|X=1)=
P(Y=3|X=1)=
(b) Are X and Y independent? (enter YES or NO)=
(c) Compute the following probabilities:
P(X+Y>4)=
P(XY=3)=
P(XY>2)=
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
probability x=1 is first column or 0.60.
The probability y=1 where x=1 is overall 0.45, so the conditional probability is 0.75.
For y=2, it is 0.05/0.60=0.0833
for y=3, it is 0.1/0.6=0.1667
for independence, p(x1 and y1)=p(x1)*p(y1)
probability of both x1 and y1=0.45 (upper left column)
probability of x1=0.6 and probability of y1=0.6.
Because that product (0.36) does not equal 0.45, they are not independent. (NO)
-
probability (X+Y)>4, look at (2,3)(3,3)(3,2), and that sum prob. is 0.25
probability (XY)=3 has two entrees, each 0.1 for a probability of 0.2
probability of (XY)>2 is 1-the complement, which is 0.45
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