00:01
Hello everyone.
00:03
Messages arrive to a computer server according to poison distribution with a mean rate of 5 per hour.
00:09
First question is what is the probability that at least three messages arrive during two hours.
00:16
No.
00:17
Now the poison formula is given by probability of x is equal to x is equal to e power minus lambda t, lambda t to the power x divided by x factorial.
00:31
Now we are asked the question for probability of x at least 3.
00:38
So it is more than 3, right? so i can rewrite this as 1 minus probability of x less than 3, which will be equal to 1 minus probability of x is equal to 0, probability of x is equal to 1, plus probability of x is equal to 1, of x is equal to 2.
00:58
Now using the formula and we are given the duration to be 2, right? so, t will be equal to.
01:09
So the value is equal to 1 minus 0 .00005 plus 0 .0045 plus 0 .0045 plus 0 .002.
01:30
So the answer for the probability of x, greater than or equal to 3 is going to be equal to 0 .997.
01:41
All right? now let's move on to the b part.
01:49
So we are given what is the probability that exactly two messages arrive in one hour.
01:54
So we have t is equal to 1 and x is equal to 2.
02:01
Now let's write it probability of x is equal to 2 is equal to e power minus 2.
02:09
We have the rate to be 5, right? so, e -par minus lambda t.
02:15
So minus 5, lambda t, to the power x is going to be 2, divided by 2 factorial.
02:26
The value here is going to be probability of exactly two majesty will be equal to 0 .08375.
02:36
All right? now the c part is, we are asked to find the length...