Stats 2A by Theresa Smith

Is the sample variance the same as the 2nd centered sample moment? Is the population variance the same as the 2nd centered population moment?

trs35 — 2021-10-11 09:08:30 UTC

I was thinking that it would be no, yes respectively. "No" for the first one because of the 1/n-1 vs 1/n. And yes for second cuz they match up. Is that logic correct?

Labsheet 3

2021-11-09 11:34:01 UTC

I dont quite understand the step 2 in 2.1. Why is it that we haev n terms of XiYi with expectation in MuXY and n^2 - n terms with expectation of MuX.MuY

Proving E(X^4)
2021-11-13 12:33:29 UTC

How do I prove that E(X^4)

2021-11-14 19:25:34 UTC

Are we getting any problem sheets after Lab 6, i.e. when the coursework is out?

Part 1, Question 1

2021-11-15 12:21:57 UTC

I am not quite sure what question 1 is asking. It does seem as though the actual question is missing.

Question 2

2021-11-15 13:45:12 UTC

Do we need to include error handling or is it safe to assume we will always be provided an nx2 matrix as input?

Question 1

2021-11-15 16:05:25 UTC

Can we use results from lab sheets immediately or do we have to derive everything to express the result?
Also, does the fact that E(X^2Y^2)

Question 1

2021-11-16 13:41:27 UTC

Where it says to show R1 is a consistent estimator of p in general, does this mean that the mean and variance are not necessarily finte?

Q1

2021-11-16 16:56:18 UTC

Do we need any other assumptions in part 1 question 1 other than E(x2y2) finite to prove it?

Example 3.7

2021-11-16 17:17:04 UTC

For Corollary 3.1 could we find a g(u) such that sigma•g’(u) = 1?

General question

2021-11-16 19:50:36 UTC

If Xn converges in law to N(mu,sigma²), does it follow that Xn/sigma converges in law to N(mu,1)?

Test Question 2

2021-11-17 15:28:10 UTC

Do we need to include the test and its output in the R Markdown file for question 2, or just have the code for the function?

Question 4

2021-11-17 16:27:43 UTC

Should we perform the simulation study for each alpha individually and repeat the code 3 times for each alpha?

Question 6

2021-11-18 11:45:56 UTC

Where does the -2 come from in the first expression (sqrt(n-2)); and why does it become sqrt(n-1) in the second?

CW file name

trs35 — 2021-11-18 12:13:15 UTC

Do our coursework files need to be named anonymously i.e. with our candidate numbers this year, or can we use our names?

Q1

2021-11-18 14:04:29 UTC

I am struggling to understand the background info section. Does it specify that Xi and Yi are i.i.d (and therefore E(X^2) and E(Y^2) are finite) or is this not given ?

As far as I can see Xi and Yi are identically distributed but I can't deduce much else.

Question 2

2021-11-18 16:42:48 UTC

For the function in Question 2, would you like our function to be defined in terms of (n, mu, var and rho) or is it preferable that we create the function in terms of an nx2 matrix, finding the nx2 matrix prior to running the function? Thanks

Question 3

2021-11-21 19:05:36 UTC

Is the process we’re trying to recreate in r…
•Get random sample of 10 rnorm bivariate data
•Work out the r1,2&3 for this sample
•Find out the mse for each r
•Then plot these 3 values against the n=10
•And repeat as n->100
I’m very confused about what it’s asking us to do

Question 3

2021-11-22 10:13:46 UTC

The plot that we have to get will have 3 lines, each of them is created by connecting a series of points lets say (x,y) for which x=mse and y=n?

Plots

2021-11-22 10:15:51 UTC

How can we adjust the size of the legend 'box' in a plot?

Q3

2021-11-22 12:08:36 UTC

when I try to use the rbivnorm in R it says that function doesn't exist

Plots

2021-11-22 13:05:58 UTC

Do we need to include the code used to show the plots or can we just show the plots? A similar question for question 2 do we need to show the code for using data_matrix or can we just show the result. As the function has to be shown I found it neater to just show the output when calling the function with data_matrix.

Question 4

2021-11-22 15:44:27 UTC

Are we treating rho as an element of continuous interval; i.e. can rho be any value between 0 and 0.9? If so, how do we denote that in R in our for loop?

Q6

2021-11-22 18:02:27 UTC

The result we are given in this question is referred to the correlation. However most of our related theory refers to mu and sigma. Can our theorems/corollaries etc be applied in this result which refers to the correlation?

2021-11-22 18:19:14 UTC

In the 2nd question of the week 6 LOIL we said that showing that g(x) is a variance stabilizing transformation is to show that sqrt(n)*[g(Xbar)-g(π)] converges in law to N(0,1). Is this always the case or it refers only to that example?

Presentation

2021-11-23 12:17:07 UTC

Will we lose presentation points if our code is really long and repetitive?
Like instead of for loops there are lots of lines of inputs etc?

R Markdown

2021-11-23 14:41:02 UTC

When I try to knit my document, it gives me an error message about the rbivnorm function that we were given. I'm not sure how to fix this.

Q5

2021-11-23 14:42:16 UTC

Do we fix rho=0.2 or let it be sequence from 0 to 0.9 when we simulate our confidence intervals?

Question 3

2021-11-23 23:44:00 UTC

Hi! Are we expected to actually derive expressions for the MSE of each R_i - as we did in Lab 3? Or instead actually calculate MSE as the sum of squared errors from our simulation?

Q5

2021-11-24 16:33:38 UTC

What do you mean by 'correct' coverage? That the confidence interval we have constructed contains the true value?

Presentation

2021-11-25 11:51:48 UTC

It says there are -3 marks for output with no R code in the file, but say we wanted to run a simulation to get a value, and then run it again after changing a variable, would it be ok to have the R code and output for the first simulation, and then say that we have changed the variable and just have the output for the second simulation, rather than having lots of R code repeated with one number changed?

Question 3

2021-11-26 11:52:45 UTC

Hi, for the nvec in question 3, would you like us to create a vector from 10 to 100, with spacing of 10, as you did in Lab 4, or would you like us to use every number from 10 to 100 in our vector. Thanks

General code repeition

2021-11-26 11:58:01 UTC

If you would like to output 3 graphs, where the parameters are changed ever so slightly, is it important to show the code? I thought that it would be okay, to just say "...using the code above, with (say) mu = 0.33. then..."

Question 4

2021-11-26 12:05:01 UTC

Why do we plot \rho between 0 and 0.9. And not 0 and 1.

Question 1

2021-11-26 14:34:10 UTC

Can we use the Strong law of large number for Question 1?

rbivnorm

2021-11-26 14:39:43 UTC

Should I set echo=TRUE for the code that generate the function rbivnorm, it is exactly the same as the code from functions.R ?

question 4

2021-11-26 15:27:36 UTC

For question 4, will we be negatively marked if we don't use a for loop for the different values of a i.e if we copy and paste our code three times with a different value of a each time, as this has proven easier than doing a loop! Thanks!

Q4) Include text and variable in graph title

2021-11-27 16:56:21 UTC

Is there any way of writing:
main=('Graph for a=' a)
where a is the value of the variable a?

e.g. Graph for a=0.2

2021-11-28 12:33:16 UTC

Corollary 3.1 is true only when we calculate confidence intervals for the mean?

Excessive Output

2021-11-28 16:08:27 UTC

On the Presentation section it says you can be marked down for excessive output? What is excessive?

Relative Merit

2021-11-28 17:01:39 UTC

What does relative merit mean? I cannot find the definition in the notes.

Q5

2021-11-28 19:42:21 UTC

Have we done anything like this in class/labs?

General Question

2021-11-29 15:37:57 UTC

If we were to copy the rbivnorm function into the markdown, then run it so it can be used in a question, can we just use the echo tool to hide it from the markdown then mention in the markdown that the function was used, or do you want to see the full function you provided in the markdown?

In Q6(ii), is it saying that the fact that the variance of x equals variance of y has given us the result that this formula follows the t-distribution for df n-1. Or is it saying that we need to use the result of variance x = variance y in our calculation of the confidence interval?

2021-11-30 17:26:39 UTC

Confidence Intervals

2021-11-30 18:05:51 UTC

Which format would you prefer we express confidence intervals in for rho:
a

Submitting Coursework

2021-12-01 08:47:16 UTC

Whenever I knit/compile my work to html and then 'print' it to pdf, the code comes out in black and white. Is this fine/acceptable?

Q4 says that the bias is never a function of sample size but the def of bias in the notes says that the bias may depend on the sample size n. Does that not mean that the bias may be a function of n?

2022-01-04 09:50:52 UTC

Why is the logit function preferred in Q9? Aren't both intervals valid as they are the intervals of examples 3.5 and 3.7?

2022-01-04 10:11:08 UTC

How many decimal places or significant figures should we round to in the exam?

2022-01-04 20:14:04 UTC

What is the purpose of calculating the ratio of likelihoods when finding the most powerful test? It seems that we calculate it to find k^* but then simply assign k^* using the fact that the test has significance level alpha (and we don't seem to actually use the likelihood ratio past the point of calculation?).

2022-01-11 14:33:06 UTC

LOIL 21st Jan

2022-01-20 21:12:47 UTC

Would you be able to review section 5.3 to 5.4.2 in the LOIL?

Stats 2A by Theresa Smith

Is the sample variance the same as the 2nd centered sample moment? Is the population variance the same as the 2nd centered population moment?

Labsheet 3

Proving E(X^4) 2021-11-13 12:33:29 UTC How do I prove that E(X^4)

Part 1, Question 1

Question 2

Question 1

Question 1

Q1

Example 3.7

General question

Test Question 2

Question 4

Question 6

CW file name

Q1

Question 2

Question 3

Question 3

Plots

Q3

Plots

Question 4

Q6

Presentation

R Markdown

Q5

Question 3

Q5

Presentation

Question 3

General code repeition

Question 4

Question 1

rbivnorm

question 4

Q4) Include text and variable in graph title

Excessive Output

Relative Merit

Q5

General Question

In Q6(ii), is it saying that the fact that the variance of x equals variance of y has given us the result that this formula follows the t-distribution for df n-1. Or is it saying that we need to use the result of variance x = variance y in our calculation of the confidence interval?

Confidence Intervals

Submitting Coursework

Q4 says that the bias is never a function of sample size but the def of bias in the notes says that the bias may depend on the sample size n. Does that not mean that the bias may be a function of n?

Why is the logit function preferred in Q9? Aren't both intervals valid as they are the intervals of examples 3.5 and 3.7?

How many decimal places or significant figures should we round to in the exam?

LOIL 21st Jan

Proving E(X^4)
2021-11-13 12:33:29 UTC

How do I prove that E(X^4)