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Suppose we toss a coin 3 times. We denote head as "H" and tail as "T". We assume the probability of head is P(H) = 0.4. Let X be the number of "H"s. 1. What are the possible values of X? Find the probability function (pf) of X, which is defined by P(X= k) for every possible value k. Check that ΣP(X= k) = 1. k

Suppose we toss a coin 3 times. We denote head as "H" and tail as "T". We assume the probability of head is P(H) = 0.4. Let X be the number of "H"s. 1. What are the possible values of X? Find the probability function (pf) of X, which is defined by P(X= k) for every possible value k. Check that ΣP(X= k) = 1. k

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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Please do the following question with program R. 

Q1. Suppose we toss a coin 3 times. We denote head as "H" and tail as "T". We assume the probability of head is P(H) = 0.4. Let X be the number of "H"s. 1. What are the possible values of X? Find the probability function (pf) of X, which is defined by P(X = k) for every possible value k. Check that Σ P(x = k) = 1. k 2. Find the cumulative distribution function (cdf) of X. 3. Calculate the expectation and the variance of X. 4. Do the followings with R: a. Create a plot of the pf of X. b. Create a plot of the cdf of X. c. Draw a random sample of size 1000 from Binomial (n = 3, p = 0.4). Then plot a histogram and calculate the sample mean and the sample variance. Comment briefly on these outputs compared to the results from question 1-3.
Transcribed Image Text:Q1. Suppose we toss a coin 3 times. We denote head as "H" and tail as "T". We assume the probability of head is P(H) = 0.4. Let X be the number of "H"s. 1. What are the possible values of X? Find the probability function (pf) of X, which is defined by P(X = k) for every possible value k. Check that Σ P(x = k) = 1. k 2. Find the cumulative distribution function (cdf) of X. 3. Calculate the expectation and the variance of X. 4. Do the followings with R: a. Create a plot of the pf of X. b. Create a plot of the cdf of X. c. Draw a random sample of size 1000 from Binomial (n = 3, p = 0.4). Then plot a histogram and calculate the sample mean and the sample variance. Comment briefly on these outputs compared to the results from question 1-3.
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