00:01
Here we are told that messages arrive according to a poisson process with a rate of 30 per minute.
00:09
For part a, we are asked what the mean time is until five messages have arrived.
00:16
We'll say x is the time until five messages.
00:23
So x is in erlang random variable with r equals 5, rate equals 30.
00:43
The expectation on x is equal to r over lambda.
00:56
Which is one -sixth of a minute, or 10 seconds.
01:03
For b, we are asked for the standard deviation of x.
01:09
This is equal to the square root of the variance of x, which is 1 over lambda.
01:24
That's r over lambda.
01:28
And again, is 1 -6th.
01:34
Now, for c, we are asked for the probability that the packet is formed in less than 10 seconds.
01:40
So that is the probability that x is less than 10, which is the same thing as the probability that the number of messages arriving within 10 seconds is at least 5, which is 1 minus the probability that the number of arriving messages is 4 or less...
