statistics

[Lucy77]

If the values of the joint probability density of Y1 and Y2 are as shown:

0 1 2 total

0 1/12 1/6 1/24 35/120
1 1/4 1/4 1/40 63/120
2 1/8 1/20 ...... 21/120
3 1/120 ...... ..... 1/20
ttl 56/120 56/120 8/120 1

whew ;-)

ok Find

a) P (Y1=0)
b) P(Y2=1 | Y1=1)
c P(Y2=1)
e Check if Y1 and Y2 are independent or dependent
f Evaluate the correlation coefficient r of y1 and y2

Thanks so much

[HallsofIvy]

Unfortunately, it is not clear from your chart whether Y1 is "across" or "down"!

Assuming that Y1 can be 0, 1, 2, or 3 (down) and that Y2 can be 0, 1, or 2, (across) then

P(Y1= 0) is just the sum of the probabilities in the first row (first column if I have Y1, Y2 backwards).

P(Y2=1 | Y1=1) is the probability in the "1 -1" cell divided by P(Y1= 1).

P(Y2= 1) is the sum of the probabilities in the second column (second row if I have Y1, Y2 backwards)