00:01
So, in this question there is the probability of density functions.
00:06
Probability of density function for exponent distribution is given as f x lambda.
00:16
So this one e minus this one.
00:21
So f x is the probability.
00:33
So f x is the probability density function.
00:49
This one is the rate parameter.
01:16
The average arrival rate.
01:20
The average arrival rate is equal to 1 divided by 2 .1 meter.
01:33
So the part 1 is a.
01:37
So we say that to find the probability of the next customer.
01:43
So p x less than equal to t.
01:48
So x is flow or follow a exponential distribution with a rate parameter.
01:55
So p, so this one is equal to 1 divided by 2 .1.
02:18
So p x less than equal to t is equal to t 0 e minus lambda x and dx.
02:32
So this is to find the probability of the next customer to arrival in the next time is t.
02:45
So you can need a calculator p x t.
02:51
So where x is the follow of exponential distribution with rate parameters.
02:58
And substitute is 1 divided by 2 .1 and t into the for form mole and calculate the integers.
03:11
Next is part b.
03:14
So the part b to find the probability of the next customer arrival time is 5 minute.
03:27
First the arrival time is a t minute.
03:34
And the arrival time is 5 minute.
03:39
So the equation change p x is greater than 5.
03:46
So arrival time is more than 5 minute.
03:50
More than 5 minute.
03:53
So we say that the x is greater than to the 5 that the complement of x is less than.
04:03
So what we write a p x greater than 5 is equal to 1 minus p x less than equal to 5.
04:15
So we know that this value is equal to 1 divided by exponential distribution is equal to 1 divided by...