Calculate the mean the variance and the standard deviation...

Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.) x: -42, -27, -15, -6 P(X = x): 0.36, 0.31, 0.24, 0.09 Mean Variance Standard deviation

Transcript

00:01 In this question, we're given a discrete probability distribution.

00:03 We want to find the mean, the variance, and the standard deviation.

00:07 So let's start with the mean.

00:09 The mean is just going to be equal to the sum of every single x times its probability p of x, which is given to us in the question.

00:29 Okay, so our first x value, let's just go ahead and type this out is 39, and p of x is 0 .56.

00:39 So we're so we multiply those together plus 20 times 0 .22 plus 9 times 0 .16 plus 6 times 0 .06.

00:59 And let's make sure real quick that these are not supposed to be negative numbers.

01:07 Okay, they are negative numbers.

01:09 So let me just go ahead and fix that real quick.

01:13 So that's just going to change with their sign.

01:14 They're all going to be negative.

01:15 And our expected value is also going to be.

01:20 Negative.

01:24 So go ahead and just enter all of that in your calculator.

01:28 So it's going to be negative 39 times 0 .56 minus 20 times 0 .22 minus 9 times 0 .16 minus 6 times 0 .06.

01:48 And i get negative 28 .04.

01:53 And that's the mean.

01:58 Next, let's talk about how to find the variance.

02:02 Standard deviation is easy to get from the variance, so you want to do the variance first.

02:08 And the formula for the variance is going to be the sum of each x value minus the mean squared times its probability.

02:17 So you kind of have to go in this order because you need the mean first in order to find variance, and you need the variance to find standard deviation.

02:26 So we're going to do, first value was negative 39 minus a negative 28 .04 squared times the probability 0 .56 plus.

02:57 And then we had negative 20 minus negative 28 .04 squared times its probability 0 .22 plus negative 9 minus negative.

03:13 28 .04 squared times 0 .16 and then plus negative 6 minus a negative 28 .04 squared times 0 .06.

03:34 And let's go ahead and calculate that.

03:36 So this one we might have to do in a couple of different steps.

03:39 We'll see.

03:40 So first we want to do negative 39 minus a negative 28 .04...