For each of the statements that follow, determine whether it is true (meaning, always true) or false (meaning, not always true), and provide a very brief explanation (not a complete proof). Here, we assume all random variables are discrete, and that all expectations are well-defined and finite. (a) Let X and Y be two binomial random variables. i. If X and Y are independent, then X + Y is also a binomial random variable. ii. If X and Y have the same parameters, n and p, then X+Y is a binomial random variable. iii. If X and Y have the same parameter p, and are independent, then X + Y is a binomial random variable. (b) Suppose that E[X] = 0. Then, X = 0 (i.e. X(w) = 0 VwN). (c) Suppose that E[X²] = 0. Then, P(X = 0) = 1.
For each of the statements that follow, determine whether it is true (meaning, always true) or false (meaning, not always true), and provide a very brief explanation (not a complete proof). Here, we assume all random variables are discrete, and that all expectations are well-defined and finite. (a) Let X and Y be two binomial random variables. i. If X and Y are independent, then X + Y is also a binomial random variable. ii. If X and Y have the same parameters, n and p, then X+Y is a binomial random variable. iii. If X and Y have the same parameter p, and are independent, then X + Y is a binomial random variable. (b) Suppose that E[X] = 0. Then, X = 0 (i.e. X(w) = 0 VwN). (c) Suppose that E[X²] = 0. Then, P(X = 0) = 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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![For each of the statements that follow, determine whether it is true (meaning, always true)
or false (meaning, not always true), and provide a very brief explanation (not a complete
proof). Here, we assume all random variables are discrete, and that all expectations are
well-defined and finite.
(a) Let X and Y be two binomial random variables.
i. If X and Y are independent, then X + Y is also a binomial random variable.
ii. If X and Y have the same parameters, n and p, then X+Y is a binomial random
variable.
iii. If X and Y have the same parameter p, and are independent, then X + Y is a
binomial random variable.
(b) Suppose that E[X] = 0. Then, X = 0 (i.e. X(w) = 0 Vw = N).
(c) Suppose that E[X²] = 0. Then, P(X = 0) = 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F153bfb9c-b05e-4b91-94e3-9e151aaf7f28%2F9cda19a2-67e7-4e06-a285-e5ebacad4f4a%2Fs604vk_processed.png&w=3840&q=75)
Transcribed Image Text:For each of the statements that follow, determine whether it is true (meaning, always true)
or false (meaning, not always true), and provide a very brief explanation (not a complete
proof). Here, we assume all random variables are discrete, and that all expectations are
well-defined and finite.
(a) Let X and Y be two binomial random variables.
i. If X and Y are independent, then X + Y is also a binomial random variable.
ii. If X and Y have the same parameters, n and p, then X+Y is a binomial random
variable.
iii. If X and Y have the same parameter p, and are independent, then X + Y is a
binomial random variable.
(b) Suppose that E[X] = 0. Then, X = 0 (i.e. X(w) = 0 Vw = N).
(c) Suppose that E[X²] = 0. Then, P(X = 0) = 1.
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