00:01
So, given that x is randomly distributed between 9 ,800, and 15 ,300, we'd have that the probability mass function for x is going to be equal to 1 over the right end point 15 ,300 minus the left end point 9 ,800.
00:23
So, let's see here, that's 1 over 300 minus 9 ,800.
00:28
That's 1 over 5 ,500.
00:34
And that is, if x is between 9 ,800 and 15 ,300.
00:45
And then we would have that the probability of a random variable being less than a particular value.
00:53
I'll say big x less than little x.
00:56
That's the cumulative distribution function is just going to be x over 5 ,500.
01:02
If actually i'll define this piecewise it's x over 5 ,500 for x between 9 ,800 and 15 ,300 it's going to be 0 for x less than or equal to 9 ,800 and it's going to be 1 for x greater than or equal to 15 ,300 so having that for part a we have that let's see here the probability that our bid is accepted is going to be equal to the probability that the competitor's bid is less than our bid.
01:45
So we know that there or that our bid is 1200 or 12 ,000 rather.
01:52
So that's just going to be using our cumulative distribution function 12 ,000 divided by 5 ,500.
02:02
That's not quite right.
02:04
One second here.
02:07
Oh, i made a silly mistake for the cumulative distribution that should be x minus 9 ,800.
02:14
In the numerator.
02:15
So that's 12 ,000 minus 9 ,800 divided by 5 ,500.
02:19
So we get a result there of 0 .4.
02:23
Then for part b, the probability that our bid is accepted, given that we bid $14 ,000 is the probability that our competitor bets or bids less than 14 ,000...