Question: If two random variables have the joint density [fleft(x_{1}, x_{2} ight)= begin{cases}x_{1} x_{2} & text { for } 0

If two random variables have the joint density

\[f\left(x_{1}, x_{2}\right)= \begin{cases}x_{1} x_{2} & \text { for } 0

find the probabilities that

(a) both random variables will take on values less than 1 ;

(b) the sum of the values taken on by the two random variables will be less than 1 .

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