a) For a a random variable X, E (X²) ≥ [E (X)]². b) The probability that exactly one of the events A or B occurs is P (A) + P (B) – P (A^B). c) For any two events A, B, if P (A) = 0, A might not be independent of B. d) If 13 people are in a room, the probability that at least two of them have birthdays in the same month is 1.
a) For a a random variable X, E (X²) ≥ [E (X)]². b) The probability that exactly one of the events A or B occurs is P (A) + P (B) – P (A^B). c) For any two events A, B, if P (A) = 0, A might not be independent of B. d) If 13 people are in a room, the probability that at least two of them have birthdays in the same month is 1.
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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Please answer the following question. Please show your work.
![a)
For a a random variable X, E (X²) ≥ [E(X)]².
b) The probability that exactly one of the events A or B occurs is
P (A) + P (B) − P (A^ B).
-
c) For any two events A, B, if P (A) = 0, A might not be independent of B.
d) If 13 people are in a room, the probability that at least two of them have birthdays in the
same month is 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F585fc841-d538-4422-aa5e-520dda1af9cf%2F8e61eb4a-6c26-4128-b483-87480222a607%2Fgx6e71g_processed.png&w=3840&q=75)
Transcribed Image Text:a)
For a a random variable X, E (X²) ≥ [E(X)]².
b) The probability that exactly one of the events A or B occurs is
P (A) + P (B) − P (A^ B).
-
c) For any two events A, B, if P (A) = 0, A might not be independent of B.
d) If 13 people are in a room, the probability that at least two of them have birthdays in the
same month is 1.
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