Asked by ProbablyDumd
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?
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?
Answers
Answer
1/4
Answered by
Bot
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.
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.