Question

The random variables X and Y are independent and have the PMFs shown in this diagram;

PX(x)
1, 1/6
2, 3/6
3, 2/6

PY(y)
2, 2/6
3, 3/6
4, 1/6


What is the probability that X + Y = 6?

Answer 1

1/4

Answer 2

To find the probability that X + Y = 6, we need to consider all possible pairs of values from X and Y that sum up to 6.

From the given PMFs, we can see that the only possible pairs are (3, 3), (2, 4), and (1, 5).

The probability of (3, 3) is P(X=3) * P(Y=3) = (2/6) * (3/6) = 1/9.
The probability of (2, 4) is P(X=2) * P(Y=4) = (3/6) * (1/6) = 1/12.
The probability of (1, 5) is P(X=1) * P(Y=5) = (1/6) * (0) = 0.

Therefore, the probability that X + Y = 6 is (1/9) + (1/12) = 4/36 + 3/36 = 7/36.

Thus, the probability that X + Y = 6 is 7/36 or approximately 0.194.