Lecture 1 30/8
Recommended problems for private study: p8, p27 and p33 in selected exercises plus this one: Let A and B be two events such that P(A)=0.6, P(B)=0.7 and P(A∪B)=0.8. Compute P(A∩B). (You can also choose among the problems at the end of chpter 2 in the textbook.) Lecture 2 31/8
Recommended problems for private study: p1, p13, p32 and p34a in selected exercises Lecture 3 1/9
Recommended problems for private study: p11 and p34b in selected exercises plus these two: 1. 65% of all email to an account is spam. The spam filter, which is not totally perfect, classifies 60% of all incoming mail as spam, and puts them in a spam folder. It turns out that 96% of the mails in the spam folder is in fact spam, whereas 4% are not. Calculate the probability that the filter correctly classifies a spam mail as such. 2. (Exam question 1b Aug. 17 2015) In a certain region 20% of the population are smokers. The probability for a smoker to get lung cancer is ten times as high as for a nonsmoker. The probability that a randomly chosen person gets lung cancer is 0.006. Compute the probability that a person who smoke gets lung cancer. Look also at the very first problem on each of the exams I have linked to on the main page. Lecture 4 6/9
Exercises here. (I think I will have time to do much of lecture 5.) Lecture 5 7/9
Exercises here. Lecture 6 12/9
Exercises for private study:
2. X and Y are exp(2) and exp(3), respectively (with the current notation, not the textbook's) and independent. Let Z = Max(X, Y) and compute the expected
value E(Z).
3. X and Y have density functions f_{X}(x) = x e^{x}, x ≥ 0
Compute the probability P(X > Y)
Lecture 7 14/9
Exercises:
2. X ∈ Bin(10, 0.1) and Y
∈ Bin(5, 0.1) are independent.
Let Z = X + 2Y. Compute
3. The independent r.v. X and Y have the density functions f_{X} (x) = x/2, 0 ≤ x ≤ 2; f_{Y} (y) = 6y(1 – y), 0 ≤ y ≤ 1. Compute the correlation coefficient ρ(X + Y, Y).
Lecture 8 20/9
Lecture 9 22/9
Exercises:
2. Recall exercise 9.3 in exercises. a) Compute the LS estimate of α. Note that it differs from the MLestimate. b) Prove that E(X^{2}) = 3α c) Compute the MKestimate of 3α using the result in b). Compare with the ML estimate of α. Lecture 10 27/9
Exercises:
2. S.20 in selected exercises Use a one sided confidence interval a ≤ μ_{AB} for μ_{AB}. Lecture 11 30/9
Exercises:
Lecture 12 3/10
Exercises:
2. Like in the previous example Joe Doe wants to test the hypothesis λ = 40, where λ is the intensity of a poisson distribution, Po(λ). He will collect one observation of X ∈ Po(λ) and reject the hypothesis if the confinence interval for λ does not contain 40. He employs the approximate "Zinterval" (i.e., normal approximation) at the approximate 95% confidence level. What is the exact (4 sign. digits) error risk for this test? (Ans.: 5.725%.) Lecture 13 7/10
Lecture 14 11/10
Lecture 15 13/10
