Given independent random variables X and Y with the following joint distribution. Find a ? b?
Last edited by Amanda2018; Oct 25th 2018 at 12:33 AM.
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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.
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?
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. $\mathcal{P}(X=1\cap Y=1)=\mathcal{P}(X=1)\cdot\mathcal{P}(Y=1)$
Thank! i work out: a = 0.4, b= 0.28