00:01
Okay, so here we want to find the cumulative distribution function for the exponential, if we didn't already know it by formula.
00:08
So with the cumulative distribution function, well, first let's write our exponential distribution should look something like lambda e to the negative lambda over or times x for some lambda that is a positive real valued number.
00:29
So if we then want to find the cumulative distribution function, we are talking the density is basically a measure of how dense probability is at a spot.
00:42
The cumulative distribution function tells us how much probability we've accumulated up to some point x.
00:49
So since we know our cdf or our pdf here, we want to find the cdf.
00:56
It's just the area from the start up to some point x.
00:59
We know we can find that just by integrating from zero up to x our density function and if we do that we're going to get negative e to the negative lambda x evaluated at our end points if we plug in our upper bound of x we get negative e to or yeah it's a little confusing here but this x is being plugged in for this x i should have made used a different variable but that's okay...