The discussion focuses on calculating probabilities from a joint probability density function (PDF) of two random variables, X and Y. The joint PDF provided is structured in a matrix format, with specific probabilities assigned to combinations of X and Y values. The participants analyze the conditional probability P(X = 1 | X + Y = 2) and the joint probability P(X <= 1 and Y <= 2), arriving at the answers of 1/2 and 1/3, respectively. The calculations involve understanding the joint distribution and applying the definitions of conditional and joint probabilities.
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X\Y 1 2
0 0.1 0.3
1 0.05 0.1
2 0.2 0.25sjaguar13 said:Given this joint PDF of X and Y:
Code:X\Y 1 2 0 0.1 0.3 1 0.05 0.1 2 0.2 0.25
So:
P(X = 1| X+Y=2) = 1/2?
P(X <= 1 and Y <= 2) = 1/3?