Question

Suppose that two electronic components in the guidance system for a missile operate independently and that each has a length of life governed by the exponential distribution with mean 1 (with measurements in hundreds of hours). Find the probability density function for the average length of life of the two components.

Answer 1

Answer:

The probability density function for the average length of life of the two components is $f(x) = 0.5e^{-0.5x}$

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following probability density:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

Each missile has a length of life governed by the exponential distribution with mean 1 (with measurements in hundreds of hours). Find the probability density function for the average length of life of the two components.

2, each with mean 1 means that $m = 2*1 = 2, \mu = \frac{1}{2} = 0.5$

So the probability density function is:

$f(x) = 0.5e^{-0.5x}$