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)

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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.
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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