Consider the following exponential probability density...

Consider the following exponential probability density function. f(x) = 1/6 e^-x/6 for x ? 0 If needed, round your answer to four decimal digits. (a) Choose the correct formula for P(x ? x0). (i) P(x ? x0) = 1 - ex0/6 (ii) P(x ? x0) = 1 + e^-x0/6 (iii) P(x ? x0) = 1 - e^-x0/6 (iv) P(x ? x0) = 1 + ex0/6 Option (iii) (b) Find P(x ? 2). (c) Find P(x ? 3). (d) Find P(x ? 5). (e) Find P(2 ? x ? 5).

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00:01 Okay, in this question, we're looking at exponential distribution.

00:03 It looks like you already did part a, so you figured out what the correct formula should be for the exponential distribution, and you have it here.

00:12 Probability that x is less than a certain value is equal to 1 minus e to the negative that value divided by 6.

00:25 And that just comes from the number that's in front of our function here.

00:29 So if we want to find probability that x is less than or equal to two, it's just going to be 1 minus e to the negative 2 .6, which is 1 minus e to the negative 1 3rd, which you can type in your calculator.

00:50 We're going to round to the nearest four decimal places.

00:55 So you might have to type the fraction first and then press a little e button.

01:01 1 third, and it's negative e to that power.

01:06 And then 1 minus that is 0 .2835.

01:24 We're going to keep doing the rest of these this way.

01:27 I think it's really easiest to do that than to try and calculate greater than.

01:32 That's just harder.

01:33 So let's calculate probability that x is less than or equal to three.

01:38 Sorry, not less than or equal to.

01:40 We want just less than.

01:43 So let's find that 1 minus e to the negative 3 over 6.

01:49 So negative 1 half.

01:56 So e to the negative 1 half, and then 1 minus that...

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