e) Find the mean, expected value, variance, and standard deviation of the above scenario.
e) Find the mean, expected value, variance, and standard deviation of the above scenario.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Styles
Scenario: A students takes the following quiz by taking random guesses.
Quiz
Instructions: Select the corresponding character to the corresponding number:
Question #1:
b)
b) во
c) 55
d) 12
e)56
f) The answer is not included.
Question #2:
b)
b) 81
c) 55
d) 72
e)56
f) The answer is not included
Question #3:
b) 5
b) B1
) 5
d) 72
e)65
f) The answer is not included
Question #4:
a)
b) 81
c) 55
d) 72
e)65
f) The answer is not included
Question #5:
a)
b) 11,
c) 15,
d) 72
e)65
The answer is not included
n FoCus
HIF
5.
5.
1 1
1 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97616da4-811a-422b-aaeb-1d2538c7eb94%2Fb097c8c6-709d-4e24-a72c-a21b40362ace%2Fmexb1mb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Styles
Scenario: A students takes the following quiz by taking random guesses.
Quiz
Instructions: Select the corresponding character to the corresponding number:
Question #1:
b)
b) во
c) 55
d) 12
e)56
f) The answer is not included.
Question #2:
b)
b) 81
c) 55
d) 72
e)56
f) The answer is not included
Question #3:
b) 5
b) B1
) 5
d) 72
e)65
f) The answer is not included
Question #4:
a)
b) 81
c) 55
d) 72
e)65
f) The answer is not included
Question #5:
a)
b) 11,
c) 15,
d) 72
e)65
The answer is not included
n FoCus
HIF
5.
5.
1 1
1 0
![e) Find the mean, expected value, variance, and standard deviation of the above scenario.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97616da4-811a-422b-aaeb-1d2538c7eb94%2Fb097c8c6-709d-4e24-a72c-a21b40362ace%2F5e3kden.jpeg&w=3840&q=75)
Transcribed Image Text:e) Find the mean, expected value, variance, and standard deviation of the above scenario.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1 : Given Information
Here in this scenario, student takes a random guesses on his quiz. The quiz contains 5 multiple choice questions with each of the question having 6 options. Exactly one of the 6 options is correct. Hence probability that the students chooses the correct answer is 1/6. And this is same for all the 5 questions.
Let we define, X be number of correct answers in the quiz.
We observe that,
- The number of trials (number of questions in the quiz) are 5, which are fixed.
- For each trial there are only two outcomes, either answer is correct or incorrect. Let us denote success as, question answered by the student is correct.
- Each trial is independent of each other, since each question is answered independently.
- The probability of success, P(success) = 1/6, is same for each trial.
That means, X satisfies all the required conditions of binomial distribution.
Hence X defined above follows a binomial distribution with number of trials, 5 and probability of success, 1/6.
The probability mass function for X is defined as,
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