Question
Download Solution PDFIf X and Y are two random variables having density function
then P(X + Y < 3) is equal to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct option is b.
Detailed Solution:
Concept:
The Joint cumulative function of two random variables X and Y is defined as
The joint CDF satisfies the following properties:
, for any y (marginal CDF of Y)
, for any x (marginal CDF of X) - P(x1 < X < x2, y1 < Y < y2) = FXY(x2, y2) - FXY(x1, y2) - FXY(x2, y1) + FXY(x1, y1)
- If X and Y are independent, then FXY(x, y) = FXY(x) FXY(y)
Two random variables X and Y are jointly continuous if there exists a nonnegative function fXY : ℝ2 → ℝ, such that for any set A ∈ ℝ2, we have
The function fXY(x, y) is called the joint probability density function (PDF) of X and Y.
Marginal PDFs
Calculation:
Last updated on Jun 13, 2025
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