Question
Find the value of the constant $k$ so that the function is a joint probability density function on $D$.$$-f(x, y)=k\left(x-x^{2}\right) e^{-2 y} ; D=\{0 \leq x \leq 1 ; 1 \leq y \leq \infty\}$$
Step 1
This means that the double integral of $f(x, y)$ over the domain $D$ should be equal to 1. Mathematically, this is represented as: $$\int_{1}^{\infty} \int_{0}^{1} -k\left(x-x^{2}\right) e^{-2 y} dx dy = 1$$ Show more…
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