00:03
In this problem, it is given that messages arrive to a computer server according to a poison distribution with a mean rate of 10 per hour.
00:14
Let x denote the number of messages arriving to the computer server per hour.
00:21
So here, lambra is 10.
00:29
As it is given that the messages arriving to the computer server have a mean rate of 10 per hour.
00:37
So here, lambda is equal.
00:39
To 10.
00:41
We have to determine the length of an interval of time such that the probability that no messages arrive during this interval is 0 .90.
00:53
That is, we have to determine the length of the interval of time.
01:00
So, t is to be found.
01:03
The probability that no messages arrive during this interval is 0 .90.
01:09
So, probability of x equal to 0 is 0 .90.
01:10
So probability of x equal to 0 is 0 .5.
01:13
0 .90.
01:17
We know that if x is a poison random variable, then probability of x equal to x is e -r raised to minus lambda t into lambda t raised to x divided by x factorial, where x ranges from 0 1 up to infinity...