Question

The number of views of a page on a Web site follows aPoisson distribution with a mean of 1.5 per minute.a. What is the probability of no views in a minute?b. What is the probability of two or fewer views in10 minutes?c. Does the answer to the previous part depend on whetherthe 10-minute period is an uninterrupted interval? Explain.d. Determine the length of a time interval such that the probabilityof no views in an interval of this length is 0.001.

Answer 1

a. P (X=0) = 0.223

b. P(X≤2) = 3.93 * 10^-5

C. No

D. t=4.6 miutes

Explanation:

a. P (X=0) =
`e^(-1.5)` = 0.223

b. P(X≤2) =
`e^(1.5 * 10) (1 + 1.5*10 + (1.5^(2) * 10^(2) )/(2) )`

= 3.93 * 10^-5

C. No, the answer to the previous part does not depend on whether the 10-minute period is an uninterrupted interval, it only depend on the uniformity of the density of views per minute ad independency of the disjoint time intervals.

D. P (X=0) =0.001

`e^(-1.5t) = 0.001\\\\-1.5t=ln(0.001)\\\\t =(-6.9)/(-1.5)`

t=4.6 miutes