X Y Y=0 Y=1 Y=2X=0 0.32 0.03 0.01X=1 0.06 0.24 0.02X=2 0.02 0.03 0.27Find P(X≤1, Y=1)
Question
Find P(X≤1, Y=1)
X Y Y=0 Y=1 Y=2
X=0 0.32 0.03 0.01
X=1 0.06 0.24 0.02
X=2 0.02 0.03 0.27
Solution
To find the probability P(X≤1, Y=1), we need to sum up the probabilities where X is less than or equal to 1 and Y is equal to 1.
From the table, we can see that the events where X≤1 and Y=1 are (X=0, Y=1) and (X=1, Y=1).
The probability of (X=0, Y=1) is 0.03 and the probability of (X=1, Y=1) is 0.24.
So, P(X≤1, Y=1) = P(X=0, Y=1) + P(X=1, Y=1) = 0.03 + 0.24 = 0.27.
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