00:01
So for this problem, i'm going to begin by noting that there is a little bit of uncertainty in the notation here.
00:07
I'm gathering by context that p of k is what is being referred to as the frequency function, which may also be referred to as the probability mass function, which would be equivalently written as p of k is equal to the probability.
00:40
I'll use pr to distinguish my indication of probability, it's the probability that our discrete random variable x is equal to a value k.
00:52
Similarly, we have capital f of k.
00:56
I'm assuming that that is the cumulative distribution function, reference, the cdf, where we have that f of k is equal to the probability that x is less than or equal to k.
01:12
So, that being said, we can see that if we take f of k, less than or equal to, or, pardon me, if we take, i need to be careful here with how i say this, if we take f of k minus f of k minus 1, we get that the result should be equal to the probability that x is less than or equal to k minus the probability that x is less than or equal to k minus 1.
01:48
Now when we express probabilities like this, we can actually put those two probabilities together...