Random variable X and Y have the joint PDFf_{XY}(x,y)=\begin{cases}c,\ x

Wierzycaz

Wierzycaz

Answered question

2021-10-23

Random variable X and Y have the joint PDF
fXY(x,y)={c, x0,y0,(x2+y)1,0,     otherwise
Find the constant c.

Answer & Explanation

wornoutwomanC

wornoutwomanC

Skilled2021-10-24Added 81 answers

The joint density function of two random variables X and Y is given below:
fXY(x,y)={c, x0,y0,(x2+y)1,0,     otherwise
c0101x2dxdy=1
0101x2dxdy=1c
01[01x2dy]dx=1c
01[y]01x2dx=1c
01(1x2)dx=1c
[x]01[x33]01=1c
(1)(13)=1c
23=1c
c=32
Thus, the value of the constant c is 32.

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