Suppose that the log-ons to a computer network follow a Poisson process with an average of 3 counts per minute. (a) What is the mean time between counts (in minutes)? (Round yours answers to 3 decimal places.) (b) What is the standard deviation between counts (in minutes)? (Round yours answers to 3 decimal places.) (c) Let denote the time between two counts. If it is an average of 3 counts per minute, find the value of such that . (Round yours answers to 4 decimal places.)

A. 0.199

B. 0.199

C. 6.0000

Step-by-step explanation:

Using the poisson distribution

f(x) = (e^-ht × (ht)^x)/x!

Where h = 3, t = 1 min

f(x) = [e^-(3× 1) ×(3×1)^x]/x!

f(1) = [e^-3 (3)]/1! = 3e^-3

= 0.1991

f(1)= 0.199

h = mean = np = 1 × 0.1991 = 0.1991

(b) for Poisson distribution

mean = standard deviation = h

h = np = 0.199

(c) we want to find x for

f(x) = P(X<x) = 0.95

So we check from the Poisson table the value of x for h= 3 gives a probability of 0.95

P(X< 6) = 0.95(approximately)

X = 6.0000

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step-by-step explanation: