00:01
It is given here that cars arrive according to a posan distribution with an average rate of 10 per hour.
00:09
So the average rate is notated as lambda.
00:14
And then we're asked for the probability of one car in the next hour, and the probability of more than 24 cars in the next six hours.
00:24
So first, let's write the probability mass function for the poson random variable.
00:30
It is equal to lambda times t to the exponent x times e to the minus lambda times t over x factorial x is any non -negative integer.
00:46
So for part a we want the probability of exactly one car in the next hour.
00:52
So our rate is defined per hour, so it's 10 per hour.
00:58
So for part a, the time duration we consider is one hour.
01:04
And so lambda times t is equal to 10.
01:12
The probability of one car is the probability that x equals 1.
01:17
And so that's 10 times e to the minus 10 over 1 factorial.
01:26
This is 0 .00045.
01:29
You can see that you have the correct answer entered here.
01:34
And then for b, we want the probability that in the next six hours, more than 24 cars arrive.
01:42
So here we are talking about a time duration of 6 hours.
01:48
In this case, lambda times t multiplies to 60...