2. Given the density f(x,y)=2(x+y), 0<x<1, 0<y<x, calculate

a) P(X<0.5, Y<0.5)

b) P(X<0.5)

c) P(Y<0.5)

Thanks~(Talking)

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- Sep 7th 2009, 05:57 PMuglingSimple question need answer #2
2. Given the density f(x,y)=2(x+y), 0<x<1, 0<y<x, calculate

a) P(X<0.5, Y<0.5)

b) P(X<0.5)

c) P(Y<0.5)

Thanks~(Talking) - Sep 8th 2009, 02:14 AMTKHunny
2a)

$\displaystyle

\int_{0}^{a}\int_{0}^{x}2\cdot(x+y)\;dy\;dx\;=\;\f rac{1}{2}

$

Solve for 'a'. - Sep 8th 2009, 04:47 AMuglingwhat's the difference between 2a and 2b?
what's the difference between 2a and 2b in this case?

- Sep 8th 2009, 05:14 AMmr fantastic
a. $\displaystyle \int_{x = 0}^{x = 1/2}\int_{y = 0}^{y = x}2 \cdot (x+y)\; dy \; dx$

b. Same as above.

c. $\displaystyle \int_{y = 0}^{y = 1/2}\int_{x = y}^{x = 1}2 \cdot (x+y)\; dx \; dy$

In each case it helps to draw the required region of integration to get the integral terminals. - Sep 8th 2009, 01:53 PMTKHunny
- Sep 8th 2009, 07:11 PMmr fantastic
- Sep 8th 2009, 08:36 PMmatheagle