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A lecturer is interested in studying the pass rate of their module. In a particular year, 20 students sit the module and 3 students fail. (a) What is a random variable? Explain why the number of student who fail the module may be considered a random variable. (b) The lecturer decides to consider multiple years that they taught the module. They believe that the number of students who fail each year can be described by the binomial distribution. Discuss whether the binomial distribution is appropriate to use here. (c) The probability distribution for a binomial random variable X~ binomial(n, p) where n is the number of trials and p the success probability, is: P(X = x) = n! k!(n − k)!P* (1 − p)n-k Explain the role of (d) After looking at the results for several years they decide that the distribution X~ binomial (20, 0.1) is appropriate for the number of students who fail the module each year. What is the mean and standard deviation of this random variable? k in the equation above. (e) The lecturer is interested in situations when no students fail. What is the probability of this occurring.

A lecturer is interested in studying the pass rate of their module. In a particular year, 20 students sit the module and 3 students fail. (a) What is a random variable? Explain why the number of student who fail the module may be considered a random variable. (b) The lecturer decides to consider multiple years that they taught the module. They believe that the number of students who fail each year can be described by the binomial distribution. Discuss whether the binomial distribution is appropriate to use here. (c) The probability distribution for a binomial random variable X~ binomial(n, p) where n is the number of trials and p the success probability, is: P(X = x) = n! k!(n − k)!P* (1 − p)n-k Explain the role of (d) After looking at the results for several years they decide that the distribution X~ binomial (20, 0.1) is appropriate for the number of students who fail the module each year. What is the mean and standard deviation of this random variable? k in the equation above. (e) The lecturer is interested in situations when no students fail. What is the probability of this occurring.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A lecturer is interested in studying the pass rate of their module. In a particular year, 20 students sit the module and 3 students fail. (a) What is a random variable? Explain why the number of student who fail the module may be considered a random variable. (b) The lecturer decides to consider multiple years that they taught the module. They believe that the number of students who fail each year can be described by the binomial distribution. Discuss whether the binomial distribution is appropriate to use here. (c) The probability distribution for a binomial random variable X ~ binomial(n, p) where n is the number of trials and p the success probability, is: n! P(X = x) = ¡p*(1 – p)"-k k!(n – k)!" Explain the role of RI in the equation above. (d) After looking at the results for several years they decide that the distribution X ~ binomial(20, 0.1) is appropriate for the number of students who fail the module each year. What is the mean and standard deviation of this random variable? (e) The lecturer is interested in situations when no students fail. What is the probability of this occurring.
Transcribed Image Text:A lecturer is interested in studying the pass rate of their module. In a particular year, 20 students sit the module and 3 students fail. (a) What is a random variable? Explain why the number of student who fail the module may be considered a random variable. (b) The lecturer decides to consider multiple years that they taught the module. They believe that the number of students who fail each year can be described by the binomial distribution. Discuss whether the binomial distribution is appropriate to use here. (c) The probability distribution for a binomial random variable X ~ binomial(n, p) where n is the number of trials and p the success probability, is: n! P(X = x) = ¡p*(1 – p)"-k k!(n – k)!" Explain the role of RI in the equation above. (d) After looking at the results for several years they decide that the distribution X ~ binomial(20, 0.1) is appropriate for the number of students who fail the module each year. What is the mean and standard deviation of this random variable? (e) The lecturer is interested in situations when no students fail. What is the probability of this occurring.
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