Question: Suppose that the login times to a computer network follows a Poisson process with an average of 4 logins per minute. a) Find the probability of exactly 6 logins in 2 minutes. b) What is the mean time between logins (in seconds)? c) What is the standard deviation of the time between logins (in seconds)? d) Determine the value of x for which the probability that the first login happens before time x seconds is exactly 0.8.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Question: Suppose that the login times to a computer network follows a Poisson process with an average of 4 logins per minute.
a) Find the probability of exactly 6 logins in 2 minutes.
b) What is the mean time between logins (in seconds)?
c) What is the standard deviation of the time between logins (in seconds)?
d) Determine the value of x for which the probability that the first login happens before time x seconds is exactly 0.8.
(Hint: In the Poisson distribution the random variable is the number of events in a time interval, such as number of logins per unit as in our question. But in the sections b, c, and d of the question, mentioned random variable is the length of time between two successive
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