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Parts IV and V please

Parts IV and V please

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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Parts IV and V please
(b) Kevin lives in a city that operates a bicycle hire scheme using a large number of bicycle 'docking stations' spread around the city. He walks past a small docking station, for up to six bicycles, each morning. He has come up with the probability mass function (p.m.f.) given in Table 1 for the distribution of the random variable X that denotes the number of bicycles available at the docking station each morning. Table 1 The p.m.f. of X x 6 012 3 4 5 p(x) 0.3 0.2 0.2 0.1 0.1 0.05 0.05 (i) What is the range of X? (ii) Explain why the p.m.f. suggested by Kevin is a valid p.m.f. (iii) What is the probability that on any particular morning, there is one bicycle at the docking station? (iv) Write down a table containing values of F(x), the cumulative distribution function (c.d.f.) of X, for x = 0, 1, 2, 3, 4, 5, 6. (v) Write the probabilities P(X < 3) and P(X ≥ 5) in terms of the c.d.f. F(x). Use the c.d.f. to calculate the values of these two probabilities.
Transcribed Image Text:(b) Kevin lives in a city that operates a bicycle hire scheme using a large number of bicycle 'docking stations' spread around the city. He walks past a small docking station, for up to six bicycles, each morning. He has come up with the probability mass function (p.m.f.) given in Table 1 for the distribution of the random variable X that denotes the number of bicycles available at the docking station each morning. Table 1 The p.m.f. of X x 6 012 3 4 5 p(x) 0.3 0.2 0.2 0.1 0.1 0.05 0.05 (i) What is the range of X? (ii) Explain why the p.m.f. suggested by Kevin is a valid p.m.f. (iii) What is the probability that on any particular morning, there is one bicycle at the docking station? (iv) Write down a table containing values of F(x), the cumulative distribution function (c.d.f.) of X, for x = 0, 1, 2, 3, 4, 5, 6. (v) Write the probabilities P(X < 3) and P(X ≥ 5) in terms of the c.d.f. F(x). Use the c.d.f. to calculate the values of these two probabilities.
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