The joint density function for x, y is given by $p ( x , y ) = \left\{ \begin{array} { c c }
\frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } & x \geq 0 , y \geq 0 \
0 & \text { otherwise }
\end{array} \right.$ Write down an iterated integral to compute the probability that x + y $\le$ 10.You do not need to do the integral.
A) $\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 10 } \frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } d ^ { } y d x$
B) $\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 10 - x } \frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } d x d y$
C) $\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 10 - x } \frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } d y d x$
D) $\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 10 - x } \frac { 1 } { 10 } e ^ { - x / 10 } e ^ { - y / 15 } d y d ^ { 2 } x$
E) $\int _ { 0 } ^ { 10 - x } \int _ { 0 } ^ { 10 } \frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } d x d y$

Question

The joint density function for x, y is given by $p ( x , y ) = \left\{ \begin{array} { c c } 
\frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } & x \geq 0 , y \geq 0 \
0 & \text { otherwise }
\end{array} \right.$ Write down an iterated integral to compute the probability that x + y $\le$ 10.You do not need to do the integral.
A) $\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 10 } \frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } d ^ { } y d x$
B) $\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 10 - x } \frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } d x d y$
C) $\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 10 - x } \frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } d y d x$
D) $\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 10 - x } \frac { 1 } { 10 } e ^ { - x / 10 } e ^ { - y / 15 } d y d ^ { 2 } x$
E) $\int _ { 0 } ^ { 10 - x } \int _ { 0 } ^ { 10 } \frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } d x d y$

Quizplus · Accepted Answer

The correct iterated integral must account for the condition $x + y \leq 10$, which limits the range of $y$ to $0$ to $10 - x$ after $x$ is chosen, hence option C correctly sets the limits of integration to reflect this condition.

The Joint Density Function for X, Y Is Given By p