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

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Probability Calculus 2020/2021, Homework 6 (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).

9. Let X be a random variable equal to −m, n and 0 with probabilities 1 m, 1

k and 1 − 1 m − 1

k, respectively. Calculate the variance of variable X2.

ANSWER:

Solution:

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10. Let X be a random variable with a CDF equal to

F (t) =





0 if t < m,

(t − m)/n if m ≤ t < m + 1, 1 if t ≥ m + 1.

Calculate the variance of variable kX + n.

ANSWER:

Solution:

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