00:02
This problem explores uniform distributions, continuous uniform distributions.
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So we can jump right into it.
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Let's say a train arrives at a station every 10 minutes.
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So this tells us that we have a uniform distribution from, let's say, 0 to 10.
00:36
And since we know that uniform distributions have the function values as 1 over b minus a, that tells us that the function value in this range from 0 to 10 is 1 over 10 minus 0.
00:52
So that means that the function value is 1 over 10, a constant.
00:57
That is the uniform distribution.
00:59
And it's zero everywhere else.
01:01
Anywhere where a uniform distribution is not defined, it is zero in that range.
01:09
So now let's go ahead and calculate the probability that a person who arrives at the station waits more than 7 minutes.
01:26
So that would tell us that x, a random variable, would be greater than or equal to 7.
01:40
And now we can integrate this over this range, right? and we know that it's greater than 7, so 7 is our lowest value, so that's going to be our left bound or lower bound.
01:49
And our upper bound here is going to be 10, as that is that is the highest value we can have in this range...