Telephone calls

The random variable that models the time between 2 phone calls has an exponential distribution with density f(x)=10exp (-10x), x is greater than 0. Calculate its distribution function and the probability that the time between calls does not exceed 5 seconds, the time between calls exceeds 15 seconds, and the time between calls will be between 5 and 15 seconds.

Correct answer:

p₁ =  -5.1847055285871E+21

Step-by-step explanation:

$$\begin{gathered} f(x)=10^{-10x} \\ F(x)=\int f(x)=-e^{10x} \\ {p}_1=F(5)-F(0) \\ {F}_0=-e^{10\cdot 0}=-1 \\ {F}_5=-e^{10\cdot 5}=-5.1847055285871\cdot 10^{21} \\ {p}_1=F_5-F_0=(-5.1847055285871\cdot 10^{21})-(-1)=-5.1847055285871\cdot 10^{21} \end{gathered}$$

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