The lifetime (in months) of two components in a certain device are random variables X X and

The lifetime (in months) of two components in a certain device are random variables $X$ and $Y$ that have joint probability distribution function

$$p(x,y)=\{\begin{array}{cc}\frac{1}{9216}(48-2x-y)& \text{if}x\ge 0,y\ge 0,2x+y\le 48\\ 0& \text{otherwise}\end{array}$$

Calculate the probability that both components function for at least 12 months without failing. Note that $p(x,y)$ is nonzero only within the triangle bounded by the coordinate axes and the line $2x+y=48$ shown in Figure 20.

Transcribed Image Text:

48 y (months) 36+ 24+ 12+ 2x+y=48 12 Region where x 212, yz 12 and 2x + y 48 24 -x (months)