(a) Describe the Binomial random variable for 4 trials. What are the possible outcomes? (b) Give an example of the Binomial r.v. associated with your Bernouilli example, and give the associated probabilities. (c) What is the expectation of that r.v.? What is the variance?
(a) Describe the Binomial random variable for 4 trials. What are the possible outcomes? (b) Give an example of the Binomial r.v. associated with your Bernouilli example, and give the associated probabilities. (c) What is the expectation of that r.v.? What is the variance?
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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Transcribed Image Text:(a) Describe the Binomial random variable for 4 trials. What are the possible outcomes?
(b) Give an example of the Binomial r.v. associated with your Bernouilli example, and
give the associated probabilities.
(c) What is the expectation of that r.v.? What is the variance?
![Binomial Random Variable
A binomial random variable is random variable that represents the number of successes in n
successive independent trials of a Bernoulli experiment. Some example uses include the number
of heads in n coin flips, the number of disk drives that crashed in a cluster of 1000 computers, and
the number of advertisements that are clicked when 40,000 are served.
If X is a Binomial random variable, we denote this X ~ Bin(n, p), where p is the probability of
success in a given trial. A binomial random variable has the following properties:
P(X = k) = (")p*(1 – p)"-k
if k e N, 0 < k < n (0 otherwise)
E\X] %3D пр
Var(X) = np(1 – p)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23388c82-c83c-484d-9931-3d5e6189a0cd%2Fd5bf9941-eb4c-4ed2-957c-1cbecbd600ae%2Fyg7kxqe_processed.png&w=3840&q=75)
Transcribed Image Text:Binomial Random Variable
A binomial random variable is random variable that represents the number of successes in n
successive independent trials of a Bernoulli experiment. Some example uses include the number
of heads in n coin flips, the number of disk drives that crashed in a cluster of 1000 computers, and
the number of advertisements that are clicked when 40,000 are served.
If X is a Binomial random variable, we denote this X ~ Bin(n, p), where p is the probability of
success in a given trial. A binomial random variable has the following properties:
P(X = k) = (")p*(1 – p)"-k
if k e N, 0 < k < n (0 otherwise)
E\X] %3D пр
Var(X) = np(1 – p)
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