contestada

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.

Respuesta :

Answer:

The value of c is 4.

Step-by-step explanation:

Consider the provided probability density function,

[tex]f(t) = ce^{-4t}[/tex]

We need to find the value of c.

According to probability density function.

[tex]\int\limits^{\infty}_{-\infty} {f(x)}} \, dx=1[/tex]

Therefore,

[tex]\int\limits^{\infty}_0 {ce^{-4t}} \, dt=1[/tex]

[tex]\frac{c[e^{-4t}]^\infty_0}{-4}=1[/tex]

[tex]\frac{-c[0-1]}{4}=1\\c=4[/tex]

Hence, the value of c is 4.