00:01
In this question, the probability mass function is given here.
00:03
So this is p .ofx.
00:05
And the probability was this is 0 .10, 0 .15, and 0 .20, 0 .25.
00:15
This is 0 .20 again.
00:19
And we have 0 .06 and then 0 .04.
00:23
Great.
00:24
So we got this table here.
00:26
So the first question, it says we have to find the calculate the probability of random variable x which is less than seven equal to five and greater than two.
00:35
So what that means between this interval we have the values x is equal to three, x is equal to four and x is equal to five.
00:45
So the probability of this event when x is equal three which is 0 .25 x is equal to four this is 0 .20 and when x is equal to 5 this is 0 .06 which is this is 45 so this is 0 .51.
01:01
This is the answer for part a.
01:03
What about for the second part? so for the cumulative function, so we have to just make a table here.
01:13
Let me just say this is x.
01:16
And we have the values.
01:18
Let's say this is okay.
01:22
We have the zero here.
01:24
One, two, three, four, five and six.
01:28
So for the cumulative function, i'm going to just denote this by the f of x.
01:33
Let me just use the green one here.
01:35
This is f of x.
01:36
This is the probability mass function here.
01:41
So this is the cumulative distribution function.
01:44
So when x is equal to zero, i mean, this is equal to also 0 .10.
01:50
And what about for it is 1? so we have to just add up this two, which is 0 .25, right? and for the next one, i'm going to add up the previous one with 0 .20.
02:01
This is 0 .45.
02:03
You just add up this number and with this number here.
02:07
And 0 .25, this is 0 .70.
02:11
This is 0 .90, 0 .96, and 1.
02:16
How we can just write this function.
02:18
This is the mass function here.
02:22
So this is the cumulative distribution function...