Mathematics 71 Online OpenStudy (gg):

i need help in probability OpenStudy (anonymous):

sure what's the problem OpenStudy (gg):

The density function of (X,Y) vector is given as $\psi _{(X,Y)} (x,y) = \left\{ \left[\begin{matrix}Axy/5 & (x,y)inT \\ 0 & (x,y)notinT\end{matrix}\right] \right\}$ , T={(x,y) | 1<x+y<2, x>0, y>0}. Prove that A=8 and find function of probability distribution and density function of Z=X+Y OpenStudy (zarkon):

$\int\limits_0^1\int\limits_{-x+1}^{-x+2}\frac{Axy}{5}dydx+\int\limits_1^2\int\limits_{0}^{-x+2}\frac{Axy}{5}dydx=\frac{A}{8}$ thus A=8 OpenStudy (zarkon):

$\int\limits_0^1\int\limits_{-x+1}^{-x+z}\frac{8xy}{5}dydx+\int\limits_1^z\int\limits_{0}^{-x+z}\frac{8xy}{5}dydx=\frac{z^4-1}{15}$ $F_Z(z)=\left\{\begin{array}{rl} 0,& \text{if }z<1 \\\frac{z^4-1}{15},& \text{if }1\leq z\leq2\\ 1,&\text{if }z>1\end{array}\right.$ OpenStudy (gg):

thanks. I was doing in the same way, but I didn't get the same result. can you show me step by step to solve the integral in the proof ? OpenStudy (zarkon):

$A\left(\int\limits_0^1\int\limits_{-x+1}^{-x+2}\frac{xy}{5}dydx+\int\limits_1^2\int\limits_{0}^{-x+2}\frac{xy}{5}dydx\right)$ Looking at the first integral... $\left.\int\limits_0^1\int\limits_{-x+1}^{-x+2}\frac{xy}{5}dydx=\int\limits_0^1\frac{xy^2}{10}\right|_{-x+1}^{-x+2}=\int\limits_0^1\left(\frac{x(-x+2)^2}{10}-\frac{x(-x+1)^2}{10}\right)dx$ $=\int\limits_0^1\left(\frac{x(x^2-4x+4)}{10}-\frac{x(x^2-2x+1)^2}{10}\right)dx$ $=\int\limits_0^1\left(\frac{x^3-4x^2+4x}{10}-\frac{x^3-2x^2+x}{10}\right)dx$ $=\left.\int\limits_0^1\frac{-2x^2+3x}{10}dx=\frac{\frac{-2}{3}x^3+\frac{3}{2}x^2}{10}\right|_0^1=\frac{-2/3+3/2}{10}=\frac{1}{12}$ I'll let you do the 2nd integral OpenStudy (gg):

I made mistakes in calculation :) I got A/24 for second integral :) thank ev ruy much :) can I send u more problems? OpenStudy (gg):

is 1 value of $F _{_{Z}}(z)$ if z>1 or if z>2? OpenStudy (zarkon):

sorry...typo... $F_Z(z)=\left\{\begin{array}{rl} 0,& \text{if }z<1 \\\frac{z^4-1}{15},& \text{if }1\leq z\leq2\\ 1,&\text{if }z>2\end{array}\right.$ OpenStudy (gg):

thanks :) would u help me with few problems more?

Latest Questions xcoledd1: i need help with a drawing
14 seconds ago 6 Replies 0 Medals Manny300303199: Does anybody know the window tint laws in Germany?
1 minute ago 4 Replies 0 Medals Jumper: You are trapped in a room with two doors. One leads to freedom, while the other leads to certain death.
2 minutes ago 46 Replies 2 Medals xcoledd1: What song is this
23 minutes ago 10 Replies 0 Medals Jumper: Colors
24 minutes ago 19 Replies 4 Medals Jumper: What is 90 u00f7 2? First to answer gets a medal ud83dude0f
18 minutes ago 16 Replies 2 Medals ShoaibChaudhry: Organisms that reproduce sexually exhibit zygotic, gametic, or sporic meiosis. One way to determine the type of life cycle an organism has is by A.
9 minutes ago 9 Replies 1 Medal noluvkid: i need some new music to listen to
28 minutes ago 18 Replies 3 Medals Stringcheese272: hows my story so far me and @SophiaL are almost done with it https://docs.google.com/document/d/1E3wpLCMlINP7aYPF-zFANfaex7151Bhxe2fB_epNOpQ/edit
17 minutes ago 5 Replies 1 Medal 5StarFab: Here is a Naruto freestyle rap i did.It does contain other anime/manga's.
16 minutes ago 11 Replies 1 Medal