- #1

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**Probability integral not converging :(**

## Homework Statement

for the joint probability density function:

[tex] f(x,y)= \begin{cases}

y & 0 \leq x, \, y\leq1 \\

\frac{1}{4} (2-y) & 0\leq x\leq 1, \, 0\leq y\leq 2 \\

0 & \text{elsewhere} \end{cases} [/tex]

find the following:

a) [itex] f_1 (x) [/itex]

b) [itex] f_2 (y) [/itex]

c) [itex] F(x,y) [/itex]

there are others but maybe this will be enough to help me see what the solution to my actual problem is, problem being that my integrals are not converging and I don't know what to do with that.

## Homework Equations

a) [tex] f_1 (x)= \int_{-\infty }^\infty \! f(x,y) \, \mathrm{d}y [/tex]

Where the integral is integrated over the range space of y.

b) [tex] f_2 (y)= \int_{-\infty }^\infty \! f(x,y) \, \mathrm{d}x [/tex]

Where the integral is integrated over the range space of x.

c) [tex] F(x,y)= \int_{-\infty }^y \int_{-\infty }^x \! f(s,t) \, \mathrm{d} s \mathrm{d} t [/tex]

Again, the lower bound is replaced by the lower bound of the range space for the appropriate variables.

## The Attempt at a Solution

a) [tex] f_1 (x) = \int_{-\infty }^1 y \, \mathrm{d}y = \frac{1}{2} y^2 |_{-\infty }^1 = \frac{1}{2} -\frac{1}{2} \infty [/tex] ???

Lets start there. My time is up on the library computer.

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