3. Consider a share that is modelled by a binomial random variable. The probability that the share increases in value by 30¢ in one month is 0.65. The probability that it decreases in value by 30¢ in one month is 0.35. The share is held for 8 months then sold. Let X denote the number of increases in the price of the share over the 8 months. (a) Find E(X) and o(X). (b) Let Y be the random variable which models the change in share price. Then Y = 0.3X – 0.3(8 – X) because 0.3X is the total increase in share price and 0.3(8 – X) is the total decrease in share price. Simplify the expression for Y in terms of X. Then using (a), find E(Y) and o(Y).
3. Consider a share that is modelled by a binomial random variable. The probability that the share increases in value by 30¢ in one month is 0.65. The probability that it decreases in value by 30¢ in one month is 0.35. The share is held for 8 months then sold. Let X denote the number of increases in the price of the share over the 8 months. (a) Find E(X) and o(X). (b) Let Y be the random variable which models the change in share price. Then Y = 0.3X – 0.3(8 – X) because 0.3X is the total increase in share price and 0.3(8 – X) is the total decrease in share price. Simplify the expression for Y in terms of X. Then using (a), find E(Y) and o(Y).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![3. Consider a share that is modelled by a binomial random variable. The
probability that the share increases in value by 30¢ in one month is
0.65. The probability that it decreases in value by 30¢ in one month
is 0.35. The share is held for 8 months then sold. Let X denote the
number of increases in the price of the share over the 8 months.
(a) Find E(X) and o(X).
(b) Let Y be the random variable which models the change in share
price. Then
Y = 0.3X – 0.3(8 – X)
because 0.3X is the total increase in share price and 0.3(8 – X)
is the total decrease in share price. Simplify the expression for Y
in terms of X. Then using (a), find E(Y) and o(Y).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8929ae3d-13b8-4550-a3ab-69af2ea4431c%2F0f5c2db7-36a4-47db-b7fa-1467f996efe7%2F1rj4d8g_processed.png&w=3840&q=75)
Transcribed Image Text:3. Consider a share that is modelled by a binomial random variable. The
probability that the share increases in value by 30¢ in one month is
0.65. The probability that it decreases in value by 30¢ in one month
is 0.35. The share is held for 8 months then sold. Let X denote the
number of increases in the price of the share over the 8 months.
(a) Find E(X) and o(X).
(b) Let Y be the random variable which models the change in share
price. Then
Y = 0.3X – 0.3(8 – X)
because 0.3X is the total increase in share price and 0.3(8 – X)
is the total decrease in share price. Simplify the expression for Y
in terms of X. Then using (a), find E(Y) and o(Y).
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