just q 4's a b and c please thank you Q1.Suppose we toss a coin 3 times. We denote head as “H" and tail as "T". We assume the probability of headisР(Н) — 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 byP(X = k)for every possible value k. Check thatEP(X = k) == 1.k2. 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 andcalculate the sample mean and the sample variance. Comment briefly on these outputs comparedto the results from question 1–3.

4. Pdf of X: Here, X follows Binomial distribution with n=3 and p=0.4.

Answered: 4. Do the followings with R: a. Create…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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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 calculate the sample mean and the sample variance. Comment briefly on these outputs comp