00:01
In this question we've got a distribution function f of x is 0 for x less than minus 1, a quarter when x is between minus 1 and 1, a half when x is between 1 and 3, three quarters when x is between 3 and 5, and 1 when x is greater than or equal to 5.
00:27
So first of all, what's the probability that x is less than or equal to 3? well that's f of 3.
00:35
So since 3 exists in this interval, that gives us three quarters.
00:42
What's the probability x equals 3? well that's going to be f of 3 minus the limit as x goes to 3 from below of f of x, remembering that f of x is the probability that x is less than or equal to x.
01:06
So this first one contains x and the second one does not contain x because it approaches, well this first one contains 3, the second one does not contain 3 because it approaches 3 from below.
01:17
So f of 3 we already said was three quarters, but as we approach 3 from below we're always in this interval, so that's a half, so that gives us a quarter.
01:29
What's the probability x is less than 3? well that's our limit as we approach 3 from below f of x, so that was our half.
01:42
What's the probability x is greater than or equal to 1? well that's 1 minus the probability x is less than 1, so 1 minus the limit as x goes to 1 from below of f of x, which is 1 minus a quarter, because when we're approaching 1 from below we're in that interval, so that's three quarters...