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Hi Elliott I don't think comments are a great idea anyway since they may be missed by your marker. You can achieve more or less the same effect...

Hi Sarah Your understanding is correct. The commentary by question number in ASET is to help you understand how the model solution satisfies the...

Hi Jenil The reason for dividing the term by 2 in the approximation is because on average each dollar paid in to the accumulation fund is only...

Hi David You're right to be confused about this. The examiners have applied the chi-squared test in a very unusual manner. Normally we would...

Hi Priyanka, I think the issue may be that you need to rearrange the equation for the time series to get the right signs for \( \alpha \) and \(...

Hi Fitting time series models can sometimes be more of an art than a science, and that is what we are seeing here. We will never observe zero...

Hi There are two things going on here, which I will cover in turn. The first is that there is a formula in the Core Reading for the Yule-Walker...

Hi The approximation you mention is central to this question. It can be written as: \( \hat S_{KM} = \prod_{t_j \le t} 1 - \hat \lambda_j...

Hi Molly This is certainly a challenging question, and quite unusual so don't get bogged down in this one. Starting from where you got to, we...

Hi Laura First thing to note is that this is an extremely hard question, the hardest on the paper in my opinion. The theme that runs through the...

Hi Jia The easiest way to calculate this is using the formula for \( \rho_k \) of an \( ARMA(1,1) \) given on page 40 of the Tables, using \(...

Hi Stephen We are in the process of updating the PBOR. Parts 1-4 are now live, and part 5 and the Y assignments should be available in...

Hi Lauren I agree the approach sometimes appears to be inconsistent. CT4 Apr 11 Q10 has come up before, and my response was that the survival...

Hi Brett The error you are making is writing p_ij(t) = exp{-mu_ij * t} (Sorry - I've altered your notation to make it clear this is a function...

Hi Edward First thing to note is that the notes are talking about empirical observation here rather than model effects, which I think is what you...

Hi Edward z is defined as: z = (A - E) / sqrt(E) ie the individual standardised deviations. The chi-squared test statistic is sum(z^2)....

Hi Edward, My apologies - I was too hasty answering your question and I set up the right formula but with the wrong justification! You need to...

Hi Edward This isn't explained in the Examiner's Report, but the reason is that we aren't dealing with a single Poisson process. This is because...

Hi Edward Your method does give the same answer eventually, but I think it's a bit less efficient. Using the Yule-Walker equations I can set up...

You've written some of that the wrong way round but I think I know what you meant to say. Let's look at the 3 probabilities to make sure you know...

Yes, that's right. Dave

Hi alpha and f model two different components of the mortality projection: f is a reduction factor, (eg 5% per annum) so the reduction factor...

Hi Brett Your immediate answer of using 1 - G(70) is the easiest trap to fall into when working with the GPD. For threshold exceedances (in this...

Hi I agree there is an apparent contradiction here, and the reason is that the first statement where the parallel is drawn with the force of...

Hi Your second line is incorrect - a Markov chain can be irreducible and not aperiodic. Indeed this question provides an example if of this....

Hi Can you be more specific when you say we are losing a term in the variance equation? Could it be because you are using the formula on p16 for...

Hi I think you may have confused the increments with the value of the process here. Consider a simple random walk defined on the integers with...

Hi For a process to be Markov, we need only know the current value of the process to predict its future states. Therefore even though the...

Just putting this in simpler terms, I could use a Cox model to show that men have higher mortality than women (say) without determining the...

Hi The Cox model is sometimes referred to as semi-parametric because it doesn't require knowledge of the baseline hazard function to fit the...

Hi Edward First thing to note is this is a hard question as noted in the Examiners' Report. We would think to difference because in part (i) of...

Hi I have a simple rule which I teach for this: For MA models, replace both bits of the cov function with the defining equation For AR models,...

Hi The alternative method for generating explicit equations for these probabilities is to solve the Kolmogorov differential equations. I haven't...

Hi The kt function describes the effect of time on mortality. As this can only be observed for historical data, some assumption has to be made...

Hi I'm not sure what formula you are looking at as I don't have immediate access to the 2019 course notes, but the latest course notes and the...

Hi Edward Yes, that's correct. I've produced a plot to demonstrate this in R using the following code. par(mfrow = c(3, 2))...

Hi The types of boundaries first come up in section 5.4 of chapter 2. The options are absorbing boundary - where the probability of leaving the...

Hi Sounds like a lovely disease doesn't it? You are right that there is a brief window when we don't know if someone will recover or not, and...

Hi The question is asking for an adaptation of the approach you mention "expected time to reach a state k". Parts (iii) and (iv) of this...

Hi The Examiners' Report misses a step here, which is to note that the probability of experiencing a period of high volatility over a period...

Hi Millie The integrating factor method is a reverse engineering of the product rule, so what we have in your example is: $$ u = e^{(\sigma +...

Hi Brett You are correct that the reason for the different results is that you have produced the simulated values in a different way....

Hi There are some recommended texts about machine learning in the course notes, but there is also a wealth of information online about all the...

Hi It's possible this was a mistake in the Examiners Report. The graph below the table in the report looks like it runs to 87 rather than 92,...

Hi Sunil, The derivation has since been added to the notes. I've reproduced it below for you (note that \( t_n \) has been replaced by \( n \)):...

Hi Sunil I can't find what you're referring to on p18 of chapter 12, but there is a similar derivation on p23. Is that what you're looking for?...

Hi ASET is not included within the CMP. You will need to order it separately. This is the link for what is included within the CMP....

Here I'm using the formula Y = T + C + S, but noting that in this case T = 0, so when we differentiate with respect to Y we get 1 = mpc + mps....

The third question is (I think) September 2010 q23. It's another funny one because usually we think of marginal revenue in terms of the effect of...

The second question is (I think) April 2015 q18. This is another tricky question. To solve it we need to think about the 45-degree diagram....

Hi - I'll answer these one by one. The first question is (I think) September 2012 q14. We are told this is an open economy (i.e. there is...

Hi For others reading this thread, the plagiarism rules are set out here (as of April 2021 - this may change in future). The key text in...

We have long answer questions going back to about 1995. Please email CB2@bpp.com if you would like us to send them to you. Dave

Using the expenditure method, gross domestic product (GDP) at market prices can be calculated as follows: GDP (market prices) = C + I + G + X - M...

Hi This was covered explicitly in CT7 but not in CB2. The opportunity cost of capital investment is the alternative best investment possibility...

Hi Bharti The formulae we need are: Y = T + C + S (note T = 0 since no government sector) W = J at equilibrium (which simplifies to I = S since...

Hi Bharti Just seen this - it's comparative advantage and terms of trade again, so similar to the other question you asked about in the other...

This is a question about comparative advantage, which is covered in chapter 24 of the textbook. You need to work out which country will produce...

The formula you want is the one for the money multiplier: m = (1 + c)/(r + c) In this case r and c are both 0.5, so to be clear r relates to the...

Hi Bharti As they have identical preferences and pay the same prices, consumer A and consumer B will get the same goods, the same total utility...

Hi Bharti You are right that they are complementary goods, and that the question doesn't give enough information to determine if they are perfect...

In answer to your second question, I'm not totally sure what you mean by "similar questions". If you mean questions where there are errors in the...

Hi Stephan Something has been pointed out to me that I missed in my original answer. The usual formula for estimating sample autocovariance is...

Hi Stephan You are essentially correct - however the missing factor is actually 1/(n-1) since the summation runs from t=2 to n (since we are...

Hi Thanks for pointing these out. 1) The question doesn't make it clear what "withdrawal" means in this sense, and it's possible to concoct...