00:01
In this question we have given, suppose that a man leaves for work before 8 am and 8 .30 am, it takes 40 to 50 minutes to reach office.
00:20
Let x denote the departure time, that is 8 o 'clock, 8 o 'clock, this is the departure time.
00:37
And we have to find the probability that the man reaches the office before 9 am.
00:47
So this is less than or equal to 60 minutes.
00:51
So it implies x is a univariant function, take it as starting point, so it will be 0 up to 30 and y is a time interval, it is a univariant function from 40 to 50 because it is the time to reach the office.
01:13
Now we have to find the probability of x plus y is less than 9 am.
01:20
So this is nothing but probability of x plus y, this will be 60 minutes from 8, so it will be less than 60.
01:27
So we will write the joint pdf function where x and y are independent.
01:44
So the function of x and y is nothing but 1 divided by 30 multiplied with 1 divided by 10.
01:56
This is 50 minus 40 and it will give you 10.
02:00
So this is nothing but 1 divided by 300 when 0 is less than x is less than 30 and 40 is less than y is less than 50.
02:09
Otherwise it will be 0.
02:14
Now we will find the value, so therefore p of x is less than 60 minus y is equal to integration from 40 to 50 and for x it is 0 to 60 minus y and the function is 1 divided by 300 dx dy...