Answer:
The probability mass function of the number of modems in use at the given time is:
[tex]P (X=x)={1000\choose x}(0.01)^{x}(1-0.01)^{1000-x};\ x=0, 1, 2, ...49[/tex]
Step-by-step explanation:
Let the random variable X = number of modems in use.
The internet provider uses 50 modems.
The number of customers served by the internet user is, n = 1000.
The probability that a customer will require an internet connection is, p = 0.01.
It is provided that the customers are independent of each other.
The random variable X satisfies all the properties of a Binomial distribution with parameters n = 1000 and p = 0.01.
The probability mass function of a Binomial distribution is:
[tex]P (X=x)={n\choose x}(p)^{x}(1-p)^{n-x};\ x=0, 1, 2, ...49[/tex]
Then the probability mass function of the number of modems in use at the given time is:
[tex]P (X=x)={1000\choose x}(0.01)^{x}(1-0.01)^{1000-x};\ x=0, 1, 2, ...49[/tex]
