00:01
Hello student let's take a look at this question.
00:03
So in this question we know that the probability density function, the probability density function, let's denote it by pdf of exponential distribution with mean beta is given by f of x is equal to 1 by beta e par 1 by beta.
00:27
So the mean of exponential distribution is beta is equal to 10 minutes which is given in the question.
00:34
So first calculating the probability for the arrival time to be less than 7 minutes.
00:40
So we will denote this by p of x less than 7.
00:43
So this is calculated as 0 to 7 f of x d x.
00:48
Let's substitute the probability density function here.
00:51
So 0 to 7 1 by beta times e power 1 by beta d x.
00:57
So this becomes, so here instead of 1, we have to take x, x by beta.
01:03
So this will be equal to integrating from 0 to 7, 1 by 10 where beta value is equal to 10, e power x by 10 dx.
01:12
So on integrating this, we get the value of the integral as 0 .503...