1. ## random variables

Given independent random variables X and Y with the following joint distribution. Find

a ?
b?

2. ## Re: random variables

Originally Posted by Amanda2018
Given independent random variables X and Y with the following joint distribution. Find

a ?
b?

I replaced the ? with letters $p~q~r~s$
\begin{align*}b+p&=0.7 \\b+r&=a \\p+0.18&=s \\r+0.18&=q \\0.7+q&=\\a+s&=1 \end{align*}

You continue.

3. ## Re: random variables

0.7 + q = 1
q = 0.3
r + 0.18 = 0.3(q)
r = 0.12

a = b + 0.12
b = 0.7 - p
for get a,b value, how i can get 'p' value?

4. ## Re: random variables

Originally Posted by Amanda2018
0.7 + q = 1
q = 0.3
r + 0.18 = 0.3(q)
r = 0.12

a = b + 0.12
b = 0.7 - p
for get a,b value, how i can get 'p' value?
Use the fact the variables are independent.
$\mathcal{P}(X=1\cap Y=1)=\mathcal{P}(X=1)\cdot\mathcal{P}(Y=1)$

5. ## Re: random variables

Thank!
i work out: a = 0.4, b= 0.28