Problem 8-4 A computer time-sharing system receives teleport inquiries at an average rate of .1 per millisecond. Find the probabilities that the number of inquiries in a particular 50-millisecond stretch will be:

 a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318

Step-by-step explanation:

Problem 8-4 A computer time-sharing system receives teleport inquiries at an average rate of .1 per millisecond. Find the probabilities that the number of inquiries in a particular 50-millisecond stretch will be:

Since we have given that

Using the poisson process, we get that

(a) less than or equal to 12

probability=  

(b) equal to 13

probability=

(c) greater than 12

probability=

(d) equal to 20

probability=

(e) between 10 and 15, inclusively

probability=

Hence, a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318

Using the Poisson distribution, the probability of x inquires in a particular 50-millisecond stretch will be:

In this problem, we are given the mean during an interval, which means that the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

The parameters are:

x is the number of successes

e = 2.71828 is the Euler number

is the mean in the given interval.

We are given an average rate of 0.1 inquires per millisecond.

50-millisecond interval, thus

Then, the probability of x inquires in a particular 50-millisecond stretch will be:

A similar problem is given at link

g

step-by-step explanation:

11

step-by-step explanation:

32.50-7.50=25

225/25=11