Suppose a playlist on a music player consists of 100 songs, of which seven are by a particular artist. Songs are played by selecting a song at random (with replacement) from the playlist. Let the random variable x represent the number of songs played until a song by this artist is played. (a) Explain why the probability distribution of x is not binomial. O For a random variable to be binomially distributed, the probability of success must be more than 20%. This is not the case for the random variable x described. O For a random variable to be binomially distributed, the trials must be independent. This is not the case for the random variable x described. O For a random variable to be binomially distributed, it must represent the number of successes in a fixed number of trials. This is not the case for the random variable x described. O For a random variable to be binomially distributed, the probability of success must be the same for all trials. This is not the case for the random variable x described. O For a random variable to be binomially distributed, each trial must always result in one of two possible outcomes, success and failure. This is not the case for the random variable x described. (b) Find the following probabilities. (Round your answers to three decimal places.) (i) P(5) (ii) P(x s 5) (iii) P(x > 5) (iv) P(x 2 5)
Suppose a playlist on a music player consists of 100 songs, of which seven are by a particular artist. Songs are played by selecting a song at random (with replacement) from the playlist. Let the random variable x represent the number of songs played until a song by this artist is played. (a) Explain why the probability distribution of x is not binomial. O For a random variable to be binomially distributed, the probability of success must be more than 20%. This is not the case for the random variable x described. O For a random variable to be binomially distributed, the trials must be independent. This is not the case for the random variable x described. O For a random variable to be binomially distributed, it must represent the number of successes in a fixed number of trials. This is not the case for the random variable x described. O For a random variable to be binomially distributed, the probability of success must be the same for all trials. This is not the case for the random variable x described. O For a random variable to be binomially distributed, each trial must always result in one of two possible outcomes, success and failure. This is not the case for the random variable x described. (b) Find the following probabilities. (Round your answers to three decimal places.) (i) P(5) (ii) P(x s 5) (iii) P(x > 5) (iv) P(x 2 5)
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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Transcribed Image Text:Suppose a playlist on a music player consists of 100 songs, of which seven are by a particular artist. Songs are played by selecting a song at random (with replacement) from the playlist. Let the random variable
x represent the number of songs played until a song by this artist is played.
(a) Explain why the probability distribution of x is not binomial.
O For a random variable to be binomially distributed, the probability of success must be more than 20%. This is not the case for the random variable x described.
O For a random variable to be binomially distributed, the trials must be independent. This is not the case for the random variable x described.
O For a random variable to be binomially distributed, it must represent the number of successes in a fixed number of trials. This is not the case for the random variable x described.
O For a random variable to be binomially distributed, the probability of success must be the same for all trials. This is not the case for the random variable x described.
O For a random variable to be binomially distributed, each trial must always result in one of two possible outcomes, success and failure. This is not the case for the random variable x described.
(b) Find the following probabilities. (Round your answers to three decimal places.)
(i) p(5)
(ii) P(x < 5)
(iii) P(x > 5)
(iv) P(x 2 5)
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