Probability A joint density function of the continuous randomvariables and is a function
Chapter 14, Problem 76(choose chapter or problem)
Probability A joint density function of the continuous random variables x and y is a function f(x, y) satisfying the following properties.
(a) \(f(x, y) \geq 0\) for all (x, y) (b) \(\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} f(x, y) d A=1\)
(c) \(P[(x, y) \in R]=\int_{R} \int f(x, y) d A\)
In Exercises 73-76, show that the function is a joint density function and find the required probability.
\(f(x, y)=\left\{\begin{array}{ll} e^{-x-y}, & x \geq 0, y \geq 0 \\ 0, & \text { elsewhere } \end{array}\right.\)
\(P(0 \leq x \leq 1, x \leq y \leq 1)\)
Text Transcription:
f(x, y) geq 0
int_{-infty}^{infty} int_{-infty}^{infty} f(x, y)
P[(x, y) in R] = int_{R} int f(x, y) dA
f(x, y) = {_0, elsewhere ^e^-x -y, x geq 0, y geq 0
P(0 leq x leq 1, x leq y leq 1)
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