00:01
Let me take notes what values are given here.
00:02
So the mean is given, which is denoted by mu.
00:06
This is 372.
00:10
And the deductible of, let me just take this note, so this is deductible of, this is 274.
00:18
And the probability is given here, which is 83 percentile, which can be written as 0 .83.
00:26
So to solve this question, first of all, let's remember the lambda value.
00:31
So the lambda value is equal to 1 over mu here.
00:34
So i can just write the lambda value as 1 over 372.
00:39
I can define the random variable x for exponential distribution, and the lambda value 1 over 372.
00:45
Let's remember the probability for this one here, when x is greater than, let's say, this is x, and the lower case, i mean the upper case x is greater than x.
00:57
We have this probability, which is 1 over, this is, i mean, the lambda times, this is e to the power negative x lambda.
01:08
This is the formula we are going to use for this question here.
01:11
So this is a condition probability.
01:13
So the given condition, we have to find the probability of random variable x is greater than lower case x and given value.
01:21
So the deductible is 274, so the random variable x should be greater than 274.
01:26
And from the condition probability, we know that their intersection is x is greater than x and x is greater than 274, which is divided by the probability of x is greater than 274.
01:43
So this ends, so we can just find this probability.
01:47
So at this step, we're going to use the integral.
01:50
So for the upper boundary, so we can just get, we can just write this probability as random variable x is greater than 274 and less than the random variable x...