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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.

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Answer:

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.

User JerryCauser
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