Suppose you accidentally closed a file on your computer and...

Suppose you accidentally closed a file on your computer and have forgotten where you saved it. Let X= the time it takes for the computer to find the file you requested when you search for it. If it takes the computer 30 milliseconds to scan the entire memory of the computer, a reasonable assumption is that X is uniformly distributed on the interval [0,30].

Transcript

00:01 Okay, so we're going to begin by writing the probability density function for a uniform random variable x on the variable on the interval, sorry, 0 to 25.

00:13 So you can apply the general formula for the density function of every uniform random variable to the given interval, which is f of x is equal to 1 over 25 for 0 is less than or equal to x, which is less than or equal to 25.

00:34 Otherwise it's zero so that's equal to 0 .0 0 .04 and 0 that's equal to x then equal to 25 okay so now the first part is going to be to integrate to determine the probability p x is greater equal to 10 which is then or equal to 20 so that's just the integral 10 -20 f -of -x d -x, which is the integral down 20 .0 .04 dx, which is equal to 0 .04, which is equal to 0 .04, with the limit is 20 and 10.

01:45 Which will just give us 0 .4.

01:50 Okay, now in part b, if to integrate to determine the probability that x was greater equal to 10.

02:04 So that is just equal to the integral of f of x from 10 to infinity, d of x, in respect to x.

02:18 So again, we're going to again, we're going to get 0 .04 x 25 10 which is equal to 0 .6 part c we have to integrate the probability density function to determine the cumulative density function so we're trying to find the cdf note that the cumulative density will either be 0 or 1 outside the region where f of x is non -zero depending on if x is a or below to non -zero region.

03:04 So what we're going to get is f of x is equal to integral, 0 to x, run the function in terms of y, and this is for zero less than equal to x, less than equal to 25.

03:22 So again, we get 0 to x, 0 .04, dy, which is equal to 0 .04, x just put plugging into balance okay so now that we have the function of x you have to combine this with the zero region of the probability density function to get the entire accumulated density function probability distribution so what we have so far is that the function of x is equal to zero 0 .0 .04 x and this this is just what we got from the previous parts.

04:10 So next square in 25, the function will be equal to 1.

04:14 It's between 0 and 25.

04:17 It'll be 0 .0 for x...

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