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

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

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

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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?

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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

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How do I prove that E(X^4)<infinity to show that prop 2.2 holds? Or do I simply assume?

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

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

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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)<infinity tell us anything about E(X^p) and E(Y^q) individually?

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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?

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

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

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

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

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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?

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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?

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

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

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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.

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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

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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

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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?

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

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

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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.

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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?

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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?

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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?

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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.

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

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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?

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

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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?

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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

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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..."

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

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

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

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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!

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Q4) Include text and variable in graph title

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Q4) Include text and variable in graph title

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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

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

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

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

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Have we done anything like this in class/labs?

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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?

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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?

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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?

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Which format would you prefer we express confidence intervals in for rho:
a<rho<b or (a,b)

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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?

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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?

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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?

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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?

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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?

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

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

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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?).

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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?).

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