Question 1136603
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See how I edited your post to make sense :


<pre>
    Let X and Y represent discrete random variables with <U>probability density function</U> {{{f(x,y)=(xy/18)}}} for x ∈ {1,2,3} and y ∈ {1,2}. 

    Compute P(X = 1 and Y = 2) and P(X +Y = 4).
</pre>

Without this editing the post MAKES NO SENSE.



<U>Solution</U>


<pre>
(a)  P(X = 1 and Y = 2) = f(1,2) = {{{(1*2)/18}}} = {{{2/18}}} = {{{1/9}}}.    <U>ANSWER</U>



(b)  Notice that  X + Y = 4 is possible only if  (X=3 AND Y=1)  OR  (X=2 AND Y=2).

     Therefore,

     P(X + Y = 4) = P(X=3 AND Y=1) + P(X=2 AND Y=2) = f(3,1) + f(2,2) = {{{(3*1)/18}}} + {{{(2*2)/18}}} = {{{(3+4)/18}}} = {{{7/18}}}.    <U>ANSWER</U>
</pre>

Solved.