Two random variables X and Y with joint density function given by:f(x,y)=\begin{cases}\frac{1}{3}(2x+4y)& 0\leq x,\leq 1\\0 & elsewhere\end{cases}Find P(x<\frac{1}{3})

banganX

banganX

Answered question

2021-05-18

Two random variables X and Y with joint density function given by:
f(x,y)={13(2x+4y)0x,10elsewhere
Find P(x<13)

Answer & Explanation

estenutC

estenutC

Skilled2021-05-19Added 81 answers

The joint density function of random variables X and Y is :
f(x,y)={13(2x+4y)0x,10otherwise
We have to find :
We have to find the value of P(X<13)
P(X<13)=013f(x,y)dx
=13013(2x+3y)dx
=13[x2+3xy]013
=13[19+y]
=9y+127

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