Question

Let T be the time (in minutes) until the first customer arrives at a restaurant. Suppose this quantity is modeled via the following probability density function, f(t) = ce−4t t > 0 0 t ≤ 0 , for some constant c > 0. (a) Find the value c.

Answer 1

The value of c is 4.

Explanation:

Consider the provided probability density function,

`f(t) = ce^(-4t)`

We need to find the value of c.

According to probability density function.

`\int\limits^(\infty)_(-\infty) {f(x)}} \, dx=1`

Therefore,

`\int\limits^(\infty)_0 {ce^(-4t)} \, dt=1`

`(c[e^(-4t)]^\infty_0)/(-4)=1`

`(-c[0-1])/(4)=1\\c=4`

Hence, the value of c is 4.