KTH Mathematics / Mathematical Statistics 
Current Information
for TCOMK3 autumn 2016
Wednesday 26/10
Thursday 13/10
Friday 7/10
Here are some old exams in English:
Friday 7/10
– confidence intervals for p Bin(n,p) and difference of such – confidence intervals for λ in Po(λ) and difference of such – some examples on power of hypothesis tests – the pvalue method. – the compilation of formulae, the numeric tables and the quick reference for the TI82STATS are now in English. Monday 3/10
Hypothesis testing using C.I., onesided and twosided. "Direct" method to construct tests with given error rate. We noted that when the distribution of interest is discrete, we have only a discrete choise of error levels. In the first example, we wanted an error level of 10%, but we had to choose either 10.34% or 4.80%. (We took the nearest, 10.34%.) By the same token, there are no CI:s with exact confidence levels for discrete distributions. I talked a little on The pvalue fallacy; If we reject the null, the error rate ("pvalue") is NOT the probability that the null is true. This is however whata majority of those who believe they understand hypothesis testing (falsely) believe. Finally, I talked a little on the power of a test, and we compared the power of two tests with the same error risk, and found that one was more powerful than the other, and hence the test to choose. Exercises for you in private as usual in the plan for lectures. Friday 30/9
Exercises for you in private as usual in the plan for lectures. Tuesday 27/9
Confidence intervals for 1. mean value of a normal distribution, σ known ("ZInterval") 2. d:o σ unknown ("TInterval") 3. approximate interval when we have many observations, not necessarily normal distribution, CLT ("ZInterval") 4. difference in mean values of normal distributions, σ:s known ("2SampleZInterval") 5. d:o when σ:s unknown but assumed equal ("2SampleTInterval, pooled=YES") (6. d:o when σ:s unknown but not assumed equal ("2SampleTInterval, pooled=NO") 7. approximate difference in mean values of a distributions, not necessarily normal distributions, unequal variances, (CLT) ("2SampleZInterval"). 8. Pairwise observations Thursday 22/9
I demonstrated LS and ML point estimators. In particular, I showed that the LS estimate of a parameter is the same as the first moment estimator. I used this to estimate the intensity of an exponential distribution. As for ML, I took a small example of a discrete variable, the exponential distribution, the binomial distribution and the general case Po(t_{i}λ), i=1....n. Tuesday 20/9
New Examiner
(It is a fact that different examiners put somewhat different emphasis on different elements of the course.) Quiz Exam 19/9
L21, L42, L43
and the time is 15 &ndash 17. Bring your calculator, but no compilation of formulae, etc. You should have got a mail about this. If you have any questions, turn to the student affairs office Wednesday 14/9
Then I defined correlation coefficient, and we looked at some examples. Note that the lectures up to and including this one cover the stuff treated on the quiz exam Sept. 19. You find exercises in the lecture plan. Monday 12/9
I talked about multivariate random variables, in particular two dimensional discrete r.v. and the convolution formula for sums. I also derived formulae for the probability function for the maximum and minimum of two discrete r.v. Next I did the corresponding for continuous variables: the convolution formula for sums, and the densities for maximum and minimum of two continuous r.v. I also demonstrated the continuous version of the law of total probability, and used it to to compute P(X > Y) when X and Y are two independent continuous r.v. In particular, I made the calculation for X ∈ exp(λ) and X ∈ exp(μ). Exercises in the lecture plan. Friday 9/9
Wednesday 7/9
I defined the distribution function for a continuous r.v. and its properties. Next I derived a general formula for the density of a function of a continuous r.v., i.e., if the density of the r.v. X is known, and Y = g(X, whow we calculate the density for Y. I gave a number of examples. As usual, You find recommended exercises for private study in the plan for lectures or directly here. Monday 5/9
I pointed out the relationship between the Poisson and exponential distribution. I used the notation SD(X) for standard deviation, whereas I see now that both Blom and "we" in exams etc. employ the notation D(X) for the standard deviation. I will stick to SD(X), since I am so used to it that I don't think I can manage to consistently use D(X). So please note that D(X) and SD(X) both denote standard deviation. Read about the binomial and poisson distributions in ch. 9 (7 in the Swedish ed), sections a) and b), i.e. "occurrence" and "exact properties". As usual, You find recommended exercises for private study in the plan for lectures or directly here. Thursday 1/9
I lectured according to the plan, and also started with the FFT, binomial and hyper geometric distributions and showed how they are implemented on a TI82 Stats. I made a punch error, it should be binompdf(20, 0.2, 5) = 0.1746. Again,You find recommended exercises for private study in the plan for lectures Wednesday 31/8
P(A) = P(AB)P(B) + P(AB*)P(B*). and gave some examples. I solved problem 1a) in the Aug.2014 exam, and proved that if the events A and B are independent, then also A and B* are independent etc. (exercise 220 in Blom.) I also demonstrated an easier version of exercise 218 and one somewhat similar to the Monty Hall problem. Again,You find recommended exercises for private study in the plan for lectures Tuesday 30/8
Note that you must register for the course in Rapp. Login with your KTHid and click "activate". The code for this course is "sanstat16". There will be a quiz exam sept. 19 at 15:00 – 17:00. It is not compulsory, but will give some bonus on the final exm. More information later. I lectured according to the plan. I had some difficulties to convince some of the students that if you toss a coin twice, the probability to get heds both times is 1/4. They insisted that the probability is 1/3. (Three possibilities, two heads, one head one tail, two tails). Actually, I don't think I managed. Anyway, tomorrow it's conditional probabilities. Salah: I will prove the this simple version of the "law of total probability": P(A) = P(AB)P(B) + P(AB*)P(B*). So you can employ this on the "MALMO" problem. Wednesday 10/8

Sidansvarig: Harald Lang Uppdaterad: 20160814 