# Excel - Statistics

#### VECTOR

##### New Member
Hi guys,,

I need you help so bad...

I dont know how I do this:

Create 100 standardized (ie subtract μ_X ̅ and divide by σ_X ̅) sample values, each based on 2 observations of exponentially distributed random variables with population averaging 2, and make histograms for the 100 standard sample values. Repeat procedure for sample sizes 5,10, 20 and 40. (Tip: Make an Excel sheet for each sample size, one with 100 sample values based on sample size 2, one with 100 sample values based on sample size 5, etc ...) Histograms should be included in the report and it should be clear which sample sizes used for the sample values on which the histograms are based.

* (You should also specify which formula you use in Excel to generate the observations of the exponentially)

#### GretaGarbo

##### Human
How far have you reached?

What do you think the idea is with this homework? What is it intended to show?

(I would prefer to do these simulations in R.)

#### VECTOR

##### New Member
How far have you reached?

What do you think the idea is with this homework? What is it intended to show?

(I would prefer to do these simulations in R.)

HI!

I have reached to the point of 0%..... The intention is to find the standardized values and then creae histograms to see what happens when the size increases (I could explain further but I am on my phone right now?

Are you Swedish?

Kindest regards

#### GretaGarbo

##### Human
Note that to get standardized values, when you take the mean of a variable its "spread" will depend on the sample size. So that:

z = (y_bar - mu)/(sd/sqrt(n))

You need to divide by the square root of the sample size.

(I have no idea how to do this in excel. I do it in R) But can you generate 2 exponetially distributed variables?

Are you Swedish?
Sorry, I don't do interviews. #### VECTOR

##### New Member
Note that to get standardized values, when you take the mean of a variable its "spread" will depend on the sample size. So that:

z = (y_bar - mu)/(sd/sqrt(n))

You need to divide by the square root of the sample size.

(I have no idea how to do this in excel. I do it in R) But can you generate 2 exponetially distributed variables?

Sorry, I don't do interviews. Alright!
Reason for why I asked if you’re Swedish is because I could then write the task to you....
otherwise I can translate it, but im
Not sure if it will be “accurate”

Wish you the best!

#### GretaGarbo

##### Human
The idea with this site is that many can contribute – and correct me if I am wrong – and that many can read and learn.

#### VECTOR

##### New Member
The idea with this site is that many can contribute – and correct me if I am wrong – and that many can read and learn.

Indeed Greta!

My bad. I will state the entire question so that all folks can see and understand in the future!
I will HOPEFULLY solve this sooner or later, or I will simply cry the year out.

The question is as follows: (If there would be any Swedes here in the fututre I will post the question in Swedish as an attatched file so that you guys would understand what we are talking about as well! )

Question/Problem

In this task, you should create 100 standardized sample means (Which you do by subtracting
μx̅ and then divide by σx̅ Or in Words > Subtract by the mean of the sample and div. by the standard deviation of the sample)
Each and every one of these should be based on two observations of exponential distrubiated and randomized populationmeans with the mean value of 2. (We do not know the observations from these two, we should find them). When we have done this, we should create histograms and later on repeat the process but with the sample sizes of 5, 10, 20 & 40.

What I found from Another forum is the following when it comes to Exponential distrubition is ;
http://nandeshwar.info/excel-2/excel-instructions-exponential-distribution/

From here, it states that "lambda" is found from 1/mean > In our case, if I then understand it right it becomes Lambda = 1/2.

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#### VECTOR

##### New Member
I repeat this question.

I will be honest right here and say just as it is; I do not really understand what you mean/ask for.
I am sorry

#### GretaGarbo

##### Human
I asked if you can generate an exponential random variable. Or can you generate a uniformly distributed random variable? The link you gave said it can be done with the command “RAND()” in excel and it said further how to transform that to the exponential distribution.

Try to do that!

Read the attachment and the text about standardisation. Notice the mu(x_bar). What does it mean?

#### VECTOR

##### New Member
I asked if you can generate an exponential random variable. Or can you generate a uniformly distributed random variable? The link you gave said it can be done with the command “RAND()” in excel and it said further how to transform that to the exponential distribution.

Answer: Yes, I will try to do just as the link stated Try to do that!

Read the attachment and the text about standardisation. Notice the mu(x_bar). What does it mean?
Answer: It is the mean of the population, which we are given in the text ---> 2
Or am I totally wrong??

Kindest regards

#### GretaGarbo

##### Human
Answer: It is the mean of the population, which we are given in the text ---> 2
Or am I totally wrong??
When the text talk about "lambda is the rate parameter or 1/mean." then it is teh population mean. Just like your stuff should have a population mean of 2.

When the test says "Step 2: Calculate Mean of the Random Numbers", then it is the sample mean.

The idea is to consider how the sample mean varies and its distribution.

- - - -

Interesting to chose an image of Isak Kruger, who went bankrupt and bankrupted many others.

#### VECTOR

##### New Member
When the text talk about "lambda is the rate parameter or 1/mean." then it is teh population mean. Just like your stuff should have a population mean of 2.

Answer: But the long term mean is the same as “my”_x. So it should be 1/2 anyway or am I totally wrong?

When the test says "Step 2: Calculate Mean of the Random Numbers", then it is the sample mean.

Answer: In other words the mean of the 100 values I get from the random test with exponential values (As the Link above guide me to) (?)
I am so sorry, it’s actuallt just a shame on how bad I am at this, even though I understand/understood all the tasks during the exam.......

The idea is to consider how the sample mean varies and its distribution.

- - - -

Interesting to chose an image of Isak Kruger, who went bankrupt and bankrupted many others.
Ivar Krueger* | ;-) | —> Depends on how you see it. The truth is what Ivar went “bankrupt” for the reason that one banking family refused to re-mortgage, thus, he was about to solve this problem when he got murdured in Paris- which set of the huge crisis and by that bankrupted practicality every Swede.
And yes, I am pretty sure he got murdered due to the circumstances
THUS- It is a Statistics forum! !

#### GretaGarbo

##### Human
If you want to ask something then you must be clear about what you are asking. (I cant find it.) So rewrite the question.

μx̅ and then divide by σx̅ Or in Words > Subtract by the mean of the sample and div. by the standard deviation of the sample
What do you think σx̅ means? It does not mean "standard deviation of the sample".

#### VECTOR

##### New Member
If you want to ask something then you must be clear about what you are asking. (I cant find it.) So rewrite the question.

What do you think σx̅ means? It does not mean "standard deviation of the sample".

My Question was when I am calculating the mean, it’s not from the 100 numbers that I get by using the formula in excel- but the mean that we are given (2).

σx̅ Is the standard deviation from the exponential distributaried numbers.

So, what I am supposed to do now is to;

1: Use the formula above that the link stated to generate the random exponential numbers.

2: Find σx̅ and ”my” x

3: Now; generate the 100 numbers and subtract / divide what is in (2) & create histograms.

When it comes to the question, they state “ each based on 2 observevations of exponential random numbers (what we generate in (1). What I do not really understand here is that it is 2 observations. Should I just create 2 “excel columns” then? Feels wrong due to that EACH standardized number should be based on the generated exponential numbers?

#### GretaGarbo

##### Human
You should:

1) generate 2 exponential distributed random numbers

2) compute the mean of that

3) standardize that

4) repeat the whole thing 1) 2) 3) 100 times and save the standardized mean

5) do the same with 3 exponential distributed random numbers etc

Show that you can do step 1)

Look in the textbook what is meant by standard error = what is the “uncertainty in the mean”?

#### VECTOR

##### New Member
You should:

1) generate 2 exponential distributed random numbers

2) compute the mean of that

3) standardize that

4) repeat the whole thing 1) 2) 3) 100 times and save the standardized mean

5) do the same with 3 exponential distributed random numbers etc

Show that you can do step 1)

Look in the textbook what is meant by standard error = what is the “uncertainty in the mean”?

Answer on the "Show step 1"

I have tried now; (When it comes to number 1). Please see the Picture. - But cant really apply the population mean of 2.
Thus, I do have a question regarding this, I am not yet sure if you understand Swedish, but in the text/question it says:

"Vart och ett baserat på 2 observationer av exponentialfördelade slumpvariabler med populationsmedelvärde 2"
Which means; Each and everyone based on 2 observations of exponential distrubuition variables with the population mean of 2"

This is where I now do not understand HOW I should plug it in.....

I am so sorry for my incapacity, it is just a total fail. Thus, I do feel even worse for the person who will have to correct it. If he has any hair now he sure will go bold afterwards….

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#### GretaGarbo

##### Human
In your formula you have = -$B$s3*LN( 1- A15) it should simply be = -2*LN( 1- A15)

So you insert “2” as the population mean. (Try some other values like 5 and 9) The mean of many values should be around 2.

Create in one row 2 uniformly distributed values. Transform that to 2 exponentially distributed values on the same excel row. Copy that downwards till 100 rows. Calculate the histogram.

(Or create the exponentially distributed values directly by = -2*LN( 1- RAND())

Do the same for 3 random values etc.