Chaya Galloway

2021-05-02

Let X and Y be jointly continuous random variables wth joint PDF is given by:
${f}_{X,Y}\left(x,y\right)=2$ where $0\le y\le x\le 1$
Find $P\left(X\ge \frac{1}{2}\right)$.

dieseisB

Let us find the value of $P\left(X\ge \frac{1}{2}\right)$.
$P\left(X\ge \frac{1}{2}\right)={\int }_{\frac{1}{2}}^{1}2dx$
$=\left[2x{\right]}_{\frac{1}{2}}^{1}$
=2-1
=1
Hence, the required value of $P\left(X\ge \frac{1}{2}\right)=1$

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