Suppose we toss a coin 3 times. We denote head as "H" and tail as "T". We assume the probability of tail is P(T) = 0.7. 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)
Suppose we toss a coin 3 times. We denote head as "H" and tail as "T". We assume the probability of tail is P(T) = 0.7. 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)
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
Please do the following questions (qu 4abc) with R. Please do the rest with full working out.
![Q1.
Suppose we toss a coin 3 times. We denote head as "H" and tail as "T". We assume the probability of tail
is P(T) = 0.7. 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
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 = 0.3).
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba18de34-fc06-47a6-b1ea-c54726b84874%2Fd10273f9-b640-4e4f-aeae-4c40275bace9%2F3twxk2d_processed.jpeg&w=3840&q=75)
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 tail
is P(T) = 0.7. 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
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 = 0.3).
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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