00:01
Hello, in this question we are dealing with the exponentially distributed data, okay, that has a mean value of 10 minutes.
00:10
View here is 10 and lambda would be 1 over 10 that would be 0 .1.
00:15
Okay, so in case of this exponentially distributed data, we have a great relationship between poisons and the exponential distribution.
00:28
Okay, sorry for the sound, just wait for five seconds.
00:34
Okay, so there is an interesting relationship between the exponential distribution and the poison distribution.
00:41
Suppose that the time that elapsed between two successive events follows the exponential distribution with a mean of mu units of time, okay, that we have given that there is 10 minutes are elapsed between two calls, on an average.
00:57
Okay.
00:58
So, also we assume that these times are independent, okay? meaning that the time between events is not affected by the times between the previous two events.
01:08
Okay, this we have already assumed.
01:11
If this assumption holds true, then the number of events per unit time will follow the poison distribution.
01:18
And what does the poison distribution says? poison distribution says that if we recall that x has the position with a mean value of lambda and we say that there are x number of events occurring in that particular time event then value would be something like this probability function would be something like this is equal to lambda to the power k e to the power minus lambda over k factorial so this would be our exponential this would be our poison distribution okay so here, in this case, as we know, that this we have calculated our mass function for probability distribution.
02:14
So as we know, we are required to calculate probability that there are more than three people's in first half hour.
02:23
So we need to calculate what? for the first part, we need to calculate our probability such that x is greater than 3.
02:32
So for that as we know probability of 0 plus probability of 1 plus probability of 2 plus probability of 3 plus probability of greater than 3, greater than or not equal to greater than 3 only.
02:47
That all must be equal to 1 and we need to calculate this probability for greater than.
02:53
So what we will do we will calculate all these 4 probability and subtract it from 1.
02:58
So probability of being 0, it will come out to we will put value of x.
03:03
To be 0.
03:04
So lambda to the power 0, e to the power minus lambda, okay? so divided by e to the power minus e to the power x, sorry, just a minute.
03:20
Let me see if i am doing any mistake, e to the power minus lambda, lambda to the power y.
03:27
No, all okay.
03:30
So, e to the power lambda over zero factorial.
03:36
So this would be 1 over e to the power 0 .1.
03:40
So this would be 1 over value is coming out to be 0 .049783.
03:46
0 .049783.
03:50
So, the probability of being one, getting one customer in 30 minutes, it would be, e to the power minus lambda over 0 to the power lambda.
04:03
So it would be 1 over e to the power 0 .1 into this was lambda.
04:10
So multiplied by 1 divided by 0 1 factor it would be so this value is coming out to be just a second let me calculate it yeah before that i would let you know there is a little small mistake here this value lambda will be we are talking about how many minutes 30 minutes now so it would be lambda here this value leverage value would be 0 .1 into 30 minutes so on an average there are 3 passengers in 30 minutes on an average three calls are to be come so this value would be not 0 .1 it would be 3 so this was the mistake because i calculated it correctly on the paper and now while explaining to you i got it raw so this is not 0 .1 it would be 0 .3 and it would the power minus lambda that would be 0.
05:04
Sorry it would be 3 only this yeah now it is correct let me yeah...