• Nie Znaleziono Wyników

Name and Surname ... Student’s number ...

N/A
N/A
Info
Pobierz
Protected

Academic year: 2021

Share "Name and Surname ... Student’s number ..."

Copied!
1
0
0

Ładowanie.... (Zobacz pełny tekst teraz)

Pobierz teraz ( 1 Stron )

Pełen tekst

(1)

Probability Calculus 2019/2020, Homework 8 (two problems)

Name and Surname ... Student’s number ...

In the problems below, please use the following: as k – the sum of digits in your student’s number; as m – the sum of the two largest digits in your student’s number;

and as n – the smallest digit in your student’s number plus 1. For example, if an index number is 609999: k = 42, m = 18, n = 1.

Please write down the solutions (transformations, substitutions etc.), and additio- nally provide the final answer in the space specified (the answer should be a number in decimal notation, rounded to four digits).

20. Let (X, Y ) be a random vector such that

P((X, Y ) = (0, 0)) = m

m + k , P((X, Y ) = (0, n)) = n m + k ,

P((X, Y ) = (n, 0)) = a

m + k , P((X, Y ) = (n, n)) = k − a − n m + k . For which value of parameter a are the variables X and Y independent?

ANSWER:

Solution:

21. Let X, Y be independent variables such that X has a uniform distribution over the interval [−m, n], and Y has an exponential distribution with parameter k. Calculate Ee

XY

.

Hint: decompose the double integral into iterated integrals with integration with respect to y inside.

ANSWER:

Solution:

Cytaty

Pobierz teraz ( PDF - 1 Stron - 30.83 KB )

Powiązane dokumenty

Mathematical Statistics 2018/2019, Homework 11 (One problem) Name and Surname ................................................... Student’s number ................

Please write down the solutions (transformations, substitutions etc.), and additio- nally provide the final answer in the space specified (the answer should be a number in

Probability Calculus 2020/2021, Homework 1 (one problem) Name and Surname ................................................... Student’s number ................

Please write down the solutions (transformations, substitutions etc.), and additio- nally provide the final answer in the space specified (the answer should be a number in

Probability Calculus 2020/2021, Homework 2 (one problem) Name and Surname ................................................... Student’s number ................

Please write down the solutions (transformations, substitutions etc.), and additio- nally provide the final answer in the space specified (the answer should be a number in

Probability Calculus 2020/2021, Homework 4 (two problems) Name and Surname ................................................... Student’s number ................

Please write down the solutions (transformations, substitutions etc.), and additio- nally provide the final answer in the space specified (the answer should be a number in

Probability Calculus 2020/2021, Homework 5 (two problems) Name and Surname ................................................... Student’s number ................

Please write down the solutions (transformations, substitutions etc.), and additio- nally provide the final answer in the space specified (the answer should be a number in

Probability Calculus 2020/2021, Homework 6 (two problems) Name and Surname ................................................... Student’s number ................

Please write down the solutions (transformations, substitutions etc.), and additio- nally provide the final answer in the space specified (the answer should be a number in

Probability Calculus 2020/2021, Homework 7 (two problems) Name and Surname ................................................... Student’s number ................

Please write down the solutions (transformations, substitutions etc.), and additio- nally provide the final answer in the space specified (the answer should be a number in

Mathematical Statistics 2019/2020, Homework 2 Name and Surname ................................................... Student’s number ................

Please write down the solutions (transformations, substitutions etc.), and additio- nally provide the final answer in the space specified (the answer should be a number in