00:01
In this exercise, we are told that the random variable x is a poisson random variable with a mean of 15, and we're asked to calculate the probabilities shown in this table.
00:15
Now, for a, the probability that x is at most 10, we could do this by hand, but it'd be pretty tedious, so let's use some software.
00:24
We can do this in excel.
00:26
In excel, we type equals to start a computation, and then we want to use the poisson distribution function.
00:32
That's it highlighted in blue here.
00:34
We select that.
00:36
We enter 10, and then we enter the mean of our distribution.
00:41
And for the cumulative argument, we enter true because we want any number of successes up to 10.
00:49
Or we want the probability that x is anything less than or equal to 10.
00:56
And we get 0 .1185 approximately.
01:08
Or b, the probability that x is equal to 13.
01:11
Now the probability mass function for the poisson random variable is given by this formula.
01:22
It's mu to the x times e to the minus mu over x factorial, and that is for x is equal to 0, 1, and so on.
01:35
So the probability that x is equal to 13 is equal to 15 to the exponent 13 times e to the minus 15 over 13 factorial...