00:01
Once again, welcome to a new problem.
00:05
This time we're dealing with probability.
00:08
And when it comes to probability, we have probability of heads, which is one half, and we also have probability of tails, which is also one half.
00:20
The purpose of probability is quantifying chance processes.
00:28
It's quantifying chance processes.
00:31
That's the purpose of probability.
00:34
So we do have a new problem.
00:37
And in this particular problem, we have x, which is the number of claims, number of claims filed by a randomly selected, a randomly selected custom.
01:00
So, and this is, this happens under homeowners, homeowners insurance, insurance policy.
01:13
And the time period that this happens is 10 years, time period.
01:20
So it happens within a framework of 10 years.
01:24
We have an actuary.
01:26
Remember, actuaries are the guys responsible for probability computations in the insurance industry.
01:33
So we have an actuary who estimates that p, which is the probability mass function of x is given by p .n plus 1, 0 .32p.
02:00
N, where n has to be greater than equal to 0 .0.
02:09
Probability, determine the probability, that a policy holder, a policyholder files at least two claims during this period.
02:29
So during the 10 -year period, i want to see that the policyholder is going to file at least two claims during this period.
02:41
So we just want to just want to just jump right into it and say p n plus 1 is 0 .32 p of n given that n is greater than 0 .3 0 .0 .2 .p0.
02:56
So when n is 0 .3p0.
03:00
So when n is 0, this is what happens.
03:04
And then when n is 2, or rather when n is 1, we have 2 right there, p of 1.
03:13
So we have 0 .32.
03:15
Squared and p of zero.
03:21
And the reason why we're saying that is because if you think about it, p of two becomes 0 .32 p of 1, but then p of 1 is this whole thing.
03:30
So it's the same as 0 .32 p of 0 .0.
03:36
And that's why we're having 0 .32 squared and p of 0.
03:41
So if we continue the process for the third year, we have, or the number 3, 0 .32, p2.
03:50
This is, it goes three times now...