The joint probability mass function of x and y is given by p(1,1)=0.3p(2,1)=0.1p(3,1)=0.1p(1,2 )=0.05p(2,2)=0p(3,2)=0.05p(1,3)=0.0 5p(2,3)=0.1p(3,3)=0.25 (a) compute the conditional mass function of y given x=2: p(y=1|x=2)= 0.5 p(y=2|x=2)= 0 p(y=3|x=2)= 0.5 (b) are x and y independent? (enter yes or no) no (c) compute the following probabilities: p(x+y> 3)= p(xy=4)= p(xy> 2)= note: you can earn partial credit on this problem. you have attempte

a)

P(Y=1|X=2) = p(2,1) = 0.1

P(Y=2|X=2) = p(2,2) = 0

P(Y=3|X=2) = p(3,2) = 0.1

b)

NO

c)

P(X+Y>3) = 0.55

P(XY=4) = 0

P(XY>2) = 0.55

Step-by-step explanation:

The joint probability table is given in the picture attached

a)

P(Y=1|X=2) = p(2,1) = 0.1

P(Y=2|X=2) = p(2,2) = 0

P(Y=3|X=2) = p(3,2) = 0.1

b)

Two events A and B are independent if, and only if,

P(A|B) = P(A) and P(B|A) = P(B)

X and Y are not independent since

P(Y=1|X=2) = p(2,1) = 0.1

whereas

P(Y=1) = 0.5

so we can see

P(Y=1|X=2)≠ P(Y=1)

c)

P(X+Y>3) = p(1,3)+p(2,2)+p(2,3)+p(3,1)+p(3,2)+p(3,3)=

0.05+0+0.1+0.1+0.05+0.25 = 0.55

P(XY=4) = p(2,2) = 0

P(XY>2) = p(1,3)+p(2,2)+p(2,3)+p(3,1)+p(3,2)+p(3,3) = 0.55

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.