A certain aircraft can only fly if both of its two engines are functioning properly. This plane is a home project and so has two different engines. The lifetimes of the engines, in years, are given by random variable X and Y and the joint probability density function of X and Y is given by $$f ( x , y ) = \left\{ \begin{array} { l l }
\frac { x ^ { 2 } + y ^ { 2 } } { 26 } & 0

Question

A certain aircraft can only fly if both of its two engines are functioning properly. This plane is a home project and so has two different engines. The lifetimes of the engines, in years, are given by random variable X and Y and the joint probability density function of X and Y is given by $$f ( x , y ) = \left\{ \begin{array} { l l } 
\frac { x ^ { 2 } + y ^ { 2 } } { 26 } & 0 < X < 2 \text { and } 0 < Y < 3 \
0 & \text { elsewhere. }
\end{array} \right.$$ 
(a) Find the probability that the airplane is capable of flying for more than 1 year.
(b) Find the marginal distribution function of Y.

Quizplus · Accepted Answer

The Answer is (a) .513
(b)

F _ { Y } ( y ) = \left\{ \begin{array} { l l } 0 & y < 0 \\frac { 24 y + 2 y ^ { 2 } } { 78 } & 0 < y < 3 \1 & \mathbf { y } > 3\end{array} ight.

A Certain Aircraft Can Only Fly If Both of Its