There are three highways in the county. The number of daily accidents that occur on these highwa

step 1 Hello there for this question. They want us to. Of the traffic accidents, the County Highway Dep

There are three highways in the county. The number of daily...

Key Concepts

Expected Value

The expected value (or mean) of a random variable represents the long-run average outcome of the random process. For a Poisson random variable, the expected value is equal to its parameter (commonly referred to as lambda), which directly indicates the average rate of occurring events.

Sum of Independent Poisson Random Variables

When independent Poisson random variables are added together, the sum is also a Poisson random variable whose parameter is the sum of the individual parameters. This key property simplifies calculations of the total expected value, as the mean of the sum is the sum of the individual means.

Poisson Distribution

The Poisson distribution models the probability of a given number of events occurring within a fixed interval of time or space, provided that these events happen with a known constant mean rate and independently of the time since the last event. It is useful for modeling counts of events such as accidents, as long as the events occur randomly and independently.

Transcript

00:01 Hello there for this question.

00:04 They want us to.

00:07 Of the traffic accidents, the county highway department recorded the following probabilities for the number of accidents per day on a certain freeway for one month.

00:21 The number of accidents per day and their corresponding probabilities are shown.

00:28 So they want us to find the mean, variance, and standard deviation.

00:34 So how are we going to go about this? so how you can solve the mean? you can solve the mean by writing the equation like this.

00:48 Where you have your x1 plus x2 plus...

00:59 How many numbers does part of your data set? divided by the number of the data set to get your mean.

01:12 Or if you have a calculator, i mean a ti -84 calculator, you just click on stats and edit.

01:21 And you know, before you write down anything, just clear out whatever numbers you have.

01:29 And add in your points.

01:34 And that's how you're able to get your mean, not your mean, but your standard deviation.

01:40 You get your means and your standard deviation that way.

01:43 To solve your variance, there's two ways you can solve it, but you can set up your formula like this.

01:51 But we're going to do certain things one at a time, so let's solve for our mean first.

01:55 So how we find our mean and standard deviation? you click on your stat button.

02:02 You go to calc.

02:06 Then you go down and click the one variable stats.

02:11 Click enter.

02:13 And then you see they got lists.

02:15 Make sure it's under the list that you wrote down your data set under.

02:21 And go down like two or three times on the button.

02:27 And once you get down to calculate, press enter.

02:31 And you will get your mean, which your mean should look something like this.

02:37 This is how your mean should look.

02:39 And when your standard deviation, since this is a sample size, we're going to go by sx.

02:47 So this one represents our sample size for our standard deviation.

02:56 If you're dealing with something like population, then you will focus on this one because this is for your population.

03:04 Just a little tidbit.

03:12 So, okay, it won't let me erase this.

03:17 Okay, it did let me erase.

03:18 Okay, so let's continue on.

03:21 So for your mean, your mean should be 0 .2.

03:31 And when it comes down to your standard deviation, so if you have a calculator, you will have your standard deviation right there.

03:40 If you don't, your standard deviation would be then your standard deviation would be your sum of x minus your mean squared.

03:56 And this includes the number of variants.

04:02 And this includes each of the numbers, so you might have to add the next one.

04:10 And so on.

04:11 And then you divide that by your sample...

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