Answer:
(a) The expected time between two successive arrivals is 1.000.
(b) The standard deviation of the time between successive arrivals is 1.000.
Step-by-step explanation:
The random variable X is defined as the time between two successive arrivals at the drive-up window of a local bank.
The random variable X follows an Exponential distribution with parameter λ = 1.
(a)
The mean or expected value of an Exponential distribution is:
[tex]\mu=E(X)=\frac{1}{\lambda}[/tex]
Compute the mean value of X as follows:
[tex]\mu=E(X)=\frac{1}{\lambda}\\\mu=\frac{1}{1}\\\mu=1[/tex]
Thus, the expected time between two successive arrivals is 1.000.
(b)
The standard deviation of an Exponential distribution is:
[tex]\sigma=\sqrt{\frac{1}{\lambda^{2}}}[/tex]
Compute the standard deviation of X as follows:
[tex]\sigma=\sqrt{\frac{1}{\lambda^{2}}}=\sqrt{\frac{1}{1^{2}}}=1[/tex]
Thus, the standard deviation of the time between successive arrivals is 1.000.
