00:01
In part a, we are given a probability function fx is x squared over 18 for x between minus 3 and 3 and it will be 0 otherwise.
00:18
So if we were to sketch the function, you can see that it will look like this.
00:36
So we want to find probability of mod of x is less than 1.
00:40
So this is the same as probability of x when we break out the mod is between minus 1 and 1.
00:48
Now minus 1 and 1 is over here.
00:50
You can see that the function is the area under curve is above the x -axis so it's fine.
00:58
So we will just integrate from minus 1 to 1 the function and that will be integrating x squared over 18 dx.
01:10
We can bring out the 1 over 18 as a constant.
01:14
So just integrating x squared, just add 1 to the power and divide by the new power.
01:22
Again i can bring down the, bring out the 1 over 3 and join the 1 over 18.
01:30
That will be 1 over 54.
01:34
Sub in the upper limit, that would be 1 cube minus sub in the lower limit minus 1 cube.
01:43
So that would be 1 out of 27.
01:51
Next one i'll find probability of x squared less than 9.
01:56
So if we were to take square root, it will be mod of less than x of 3.
02:03
And so opening up that will be minus 3 less than x and x less than 3.
02:14
So you can see that the entire probability function is defined from minus 3 to 3.
02:21
So the entire area under graph would be total of 1.
02:25
So do not need to even integrate...