00:01
Here we are told that there's an average of 30 patients dying in a single day in a large hospital.
00:07
And for part a we're asked to find the probability distribution, expected value, and variance of the number of patients who died in one day.
00:16
So let's denote the random variable that is the number of patients who die in a given day as x.
00:22
Now when we have some random phenomenon occurring, such as patients dying in the hospital, and we have a steady average rate and we know what it is, then the number of patients that die in a given duration can be modeled as a poisson random variable.
00:38
So here we can say x is approximately a poisson with an average rate of occurrence of 30 per day.
00:53
So for part a, probability distribution where the poisson random variable is given by this formula.
01:13
So for our particular distribution, the probability mass function is 30 to the exponent x times e to the minus 30 over x factorial, where x is any non -negative integer.
01:31
The expected value in this case is lambda, which is 30, and the variance for a poisson random variable is also lambda.
01:57
So the expected value and the variance for a poisson distribution are equal.
02:07
And then for part b we're asked the same question, but the duration is five days instead of one day.
02:14
So really i use the average rate here, lambda, but we should be using the mean...