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Hello 1. Why is 2P73 * 4P75 = exp(-2 * 0.02) * exp(-4 * 0.04) used instead of 3P73 * 3P76 = exp(-3 * 0.02) * exp (-3 * 0.04)?? This is because I...

Hello Good spot, this a typo in the Examiners' Report. It should be -2 in the first formula. Andy

I believe so. As far as I'm aware, it isn't happening in April.

Hello Thanks for point this out, well spotted! Yes that's a typo, it should be +1.009. Thanks Andy

Hello The t-result we use in linear regression comes from assuming normality of the data - which is not something that we assume in general for a...

Hi f12378 When there are two policies, if either one terminates then we go to there being one. As each one terminates with a rate of 0.2, the...

Hi f12378 That is indeed the rule of thumb we give in CS1. That's a fair point. Looking at this, the approximation seems pretty close for this...

Hi Rahul I'm not aware of this being an issue - it has come up before specifically when a transition diagram was asked for, in which case I would...

Hi Michael I'd approach this by trying to think about the different possible transitions. Say we are currently in state i. This means there...

Hi Rahul This is a tricky concept and Core Reading doesn't go into any detail here! This section is describing parameter estimation using the...

Hi Hariram Double check any information that you receive from the IFoA; however, as far as I know, the April 2024 CS2 exams will be sat in the...

Hello (n-1) choose (n/2 - 1) is (n-1)! / [(n/2 - 1)! * (n/2)!]. Let's call this A. (n) choose (n/2) is n! / [(n/2)! * (n/2)!]. Let's call this...

Paper A is 70% and Paper B is 30%. This is set out here: https://actuaries.org.uk/qualify/after-exams/marking-guidelines/

Hi Fiorentinaa You are correct, it should just become tpx^24 as you say. As far as I can tell, that's what's in the solutions. Would you be...

Hi Rahul Say mu(x) = 0.007377, n = 100,000 and we are considering the period of 1 day. Assuming 365 days in a year, then h is 1/365. The number...

Hi James Unfortunately, as far as I'm aware, you can't use any drawing functionality unless this has been specifically agreed with the IFoA....

Hi James For a time-homogeneous MJP, it isn't that we can't / don't know the actual times but rather that the actual start and end times don't...

Hi Rahul Yes that's correct. All the best Andy

This is calculated in a separate question at the start of page 19. Andy

Hello Here we're interpolating between Phi(1.23) and Phi(1.24) to estimate Phi(1.23329). There are a few ways to write out the interpolation,...

Hello Here the Examiners wanted us to calculate the probability that an individual withdrawal is less than 1,400. Indeed we can answer this...

Hello The kt have been calculated using the formula given on the bottom of page 17. For example: k_2010^ = -4.34281 - (-4.37407) + -4.19971 -...

Hello That's right, there are two exams for CS2, Paper A, which is completed in Word, and Paper B which is done in R (although what you actually...

Hi James P(0) is the identity matrix. So, using your second equation, \( P'(t) |_{t=0} = A * P(0) = A \). Hope this helps! Andy

Hi Harj The possible options for Di are 0 or 1. The possible values for Vi are 0 to bi - ai. Let's consider the possible values for Di. If Di...

Hi Harj By definition: d/dt tpx = lim(dt -> 0+) ((t+dt)px - tpx) / dt Rearranging the first equation you quoted gives: ((t+dt)px - tpx) = -...

Hello Personally I'd be doing the latter, clearly stating the formula that I'm using for the individual standardised deviations and then copying...

Hello That's right, it hasn't been examined on any CS2B paper so far. There is also very limited R code (basically none) in the Core Reading for...

Hello I wouldn't expect the questions in the paper B exam to necessarily relate to exact scenarios you've come across before. It is likely...

Hello The only mention of font colour that I can see in the handbook is the following paragraph on page 7: 11. You must ensure the content of...

Hello You've shown that d(tqx) / dt evaluated at t = 0 is equal to mu_x, which is correct as it is 0px * mu_x and 0px is 1. In your final line,...

Hello Absolutely, it's this document here: https://actuaries.org.uk/media/iymhibw0/r-for-cs1b-and-cs2b-for-2023-exams.docx Andy

Hello 1) I(k) (for k not equal to 0) processes are special types of non-stationary processes where we can obtain stationarity by differencing....

Hello Z is a discrete RV that can take the values 0 or 30 with probabilities 0.8 and 0.2, respectively. For a discrete RV, we have: E[h(Z)] =...

Hello 1. Remember with the GPD that we are working with a threshold exceedance amount. So, if X is the underlying currency loss then we have W...

Hello If you run the library command and it can't find the package, then it hasn't been installed. What happens when you try to run:...

Hello This is because X is defined as the number of policies with up to 2 claims (as per the paragraph preceding part (i)). Hope this helps! Andy

Hello The formula here is: Var(Z) = E[Z^2] - E[Z]^2 E[Z] = 0.2 * 30 = 6. Hope this helps! Andy

Hello Smoothness test Imagine the extreme where we just take the crude rates as the graduated rates (this is undergraduated). Say that the...

Hello The relevant results for the theoretical ACF and PACF are as follows (assuming we are considering a stationary series): For an AR(p)...

Hello An invertible MA can be written as an AR of infinite order. A stationary AR can be written as an MA of infinite order. An ARMA process is...

Hello Here is one site I found: https://smac-group.github.io/ts/proofs.html#appendixa All the best Andy

Hello 1. For it to be Markov, this needs to be true regardless of the value of e_(n-2). So, showing it works only when it is 0 means it can't be...

Hello 2. For the time set, remember that the stochastic process consists of a collection of random variables, one for each time in the time set....

The measure of purity (or perhaps more accurately, impurity) for a particular node j is given by: sum(k = 1, K) [pjk(1-pjk))] where pjk is the...

Hello See some comments below: 4. As Andrea says, a group of positive signs is a run of 1 or more consecutive positive deviations. Does her...

Hello 1. Again, sorry but not entirely sure what you're asking here, could you try rephrasing it? In both cases, mu_ij refers to the transition...

Hi Ykai 1. Apologies, there is actually a typo in the question. The first line should read: .... Poisson distribution with parameter mu. the...

Hello Please see some comments below: 1. I'm not entirely sure what you mean here. The equations are derived by considering different ways of...

Hello See some comments below: 1. It isn't weakly stationary. The question asks us to state whether it is or isn't, not prove that it is. 2....

Hello Remember that age is continuous, so the force of mortality from age 70 to 75 is 0.02 but then from just above 75 to 80 is 0.04, as used in...

Hello In my view, the easiest way to tackle this question is to first covert the series into its AR representation. Remember two key results...

Hello 1. The period of a state is the highest common factor (HCF) of the possible return times to that state (ie the set of times n such that...

Hi Ykai I'm afraid I'm not sure. I would try googling the help pages of VitalSource or contacting them directly. All the best Andy

Hi Ykai 1. the definition of an o(t) function is in the next paragraph of the notes. 2. Firstly it's worth remembering some of the notation. Mu...

Hi Iamminime Good question! This is similar to the idea of thinning a Poisson process. Say we have that Xj takes the value 0 with probability...

Hi Iamminime In this case, we're told that the population remains approximately constant at 7500 over the course of the 5 years. So the number...

Hi Adam I would stick with solving simultaneous equations as the method of taking a matrix inverse is not covered in the Core Reading. All the...

Hi Alex Although you're getting warning messages, it does seem to say that the packages were installed. What happens if you run:...

Hi Akansha The contribution to the partial likelihood when someone experiences the event of interest is: hazard of person who experienced the...

Hi Jamie It's worth first writing down the defining equation for Yt, if you haven't already done so for the prior parts. As: \(Y_t = X_t -...

Hello This is because we're told that the long-term probability of being in the 15% state is the same as the long-term probability of being in...

Hi Patrick Yes I understand it is perfectly fine to use Excel for these calculations, just make sure that you still show your workings in Word....

Hi Alex Ruin theory as a topic is now in Subject CM2. It is briefly mentioned in CS2 but not covered in any real detail. All the best Andy

Hi George Unless the question specifies a particular approach or method should be used (which I would not expect to the be case), then I...

Hi Patrick If you see a question like this then assume stationarity. We wouldn't be able to fit the model otherwise. Hope this helps Andy

Hello My recommendation would be to draw out a timeline of ages. For example: 54.5 ----- 55 ----- 55.5 ----- 56 ----- 56.5 ----- 57 Let's say...

Hello The weights come from the linearity assumption. We have the values at time 0 and time 1 (P82(0) and P82(1)). We want to calculate the...

Hello If we say: S = X1 + X2 + ... + XN where Xi = Ci + Ei Ci is the claim amount of the ith claim Ei is the expense amount of the ith claim N...

Hi George I would not be using any packages not in the list of required packages for the exam. All the best Andy

Hi George I would not be using any packages outside of those listed as required for the exam. This list will be in the 2023 CS2 guide that will...

Hi George Looks like you may be mixing up Markov chains with Markov jump processes. Here we have continuous rather than discrete time. I think...

Hi Jamie In this example, we're trying to calculate the probability \( p_{0,2}^{(3)} \). In other words, the probability that an individual...

Hi Molly No problem! The idea can be extended to more complex models. All the best Andy

Hi Molly That's right, the portmanteau test is also used to investigate whether the residuals appear to form a sample from a white noise process....

Hi Molly These look correct to me. Note that we get to these by assuming uniform birthdays of the population over the relevant intervals. Andy

Hi Molly This is a pretty standard assumption. We make this assumption in the 2014 question also. For Company C for example we assume that the...

Hi j98 Packages are regularly updated and are then sometimes no longer supported on older versions of R. It's possible that randomForest is no...

Hi Molly As the aim is to have M(Z_t) = N(Z_t-1) + e_t where Z_t = (Xt, Yt), it's probably a good idea for us to rearrange the equations to have...

Hi Molly choose(n+1, n) = (n+1)! / (n! * 1!) = (n+1) the 3^2 gives the 9 and then we have (1/4)^2 * (1/4)^n = 4^(-n-2) Hope this helps! Andy

Hi Molly N is a Poisson RV but the parameter is treated as a random variable. So: N | mu = a ~ Poi(a) or N | mu ~ Poi(mu) The unconditional...

Hi Molly Stationary distributions are covered in the context of Chapter 2, Markov chains, rather than Markov jump processes. Markov chains don't...

Hi Molly The question may make it clear what they want you to use by eg getting you to write down the relevant differential or integral equation...

Hi j98 I can't completely guarantee what will be on the exam though I would be surprised if the exam required use of a package not on the list of...

Hi Molly Say we're fitting an AR(2) model to some data, ie we're saying that we think that the data can be modeled as follows: Xt = a1 Xt-1 + a2...

Hi Molly If we have a time series equation written in terms of the backwards shift operator then yes pulling out a factor of (1-B) from the...

Hi Molly Which part of the question are you looking at, part (i) or part (ii)? Andy

Hi Molly The time series equation is: \( X_t = \alpha X_{t-1} + e_t \) There are two random components to the construction of \( X_t \), there...

Hi Jia The number of possible pairings that could result in a new infection is i * (10 - i). The total number of possible pairings is 10C2 = 45....

Hi Nanaba Well spotted! Looks to me to be a mistake in the given sample numbers. I can't see why the sample PACF at lag 2 wouldn't be 0.335....

Hi Molly When faced with this question it is often a good idea to think about the type of paths for the given scenario. In order for the person...

Hi Jia This looks find to me. Next time could you just copy and paste into the forum post? Thanks! Andy

Hi Peter I think you may be using the rows instead of the columns of P in the matrix multiplication. When we have <row vector> * <matrix>, the...

Hi Molly p_ij(0,t) is not necessarily 0. This is the probability of going from State i to State j from time 0 to time t, which may be possible....

Hi Molly The boundary condition is one of the following, depending on whether the destination state is the same as the starting state: p_ii(0) =...

Hi Molly In this example, we're using the fact that we have a difference equation for the rho_k's. We want to solve this difference equation to...

Hi Molly As you point out, the problem is the 0.1n. If we just had: X_n = 0.5 * X_(n-1) + e_n then this is a stationary AR(1) process....

Hi Molly The formula given in 12.2 is k_(t+1) = k_t + mu + e_t which can be rearranged to; k_(t+1) - k_t = mu + e_t This can also be written...

Hi Molly Thanks for pointing this out, I agree that the Bj as given in this solution don't look right. In general, the Bj are meant to represent...

Hello Priyanka The main point here is that the conditional mean of Y decreases as the value of x increases. Assuming that this remains true as...