Question

Part I: Ene concept of a percentile (equivalently, quantile) is very important in data analysis. It applies to both samples and distributions. So, let's get some wi practice with them, starting with the binomial distribution. In prelab, you learned that the function gbinom(p. size prob) gives the p-th quantile of the binomial distribution with parameters n - size and pi prob. tocus on the binomial distribution with parameters n-10 and pi-0.3.Then, the 38th percentile (or 0.38 quantile) of that distribution is qbinom (0.38, 10, 0.3) # 2 , le , the area to the left of x-2, under that binomi I dist bution is 0.38 (or 38%). height" of p x) in You also learned from prelah2 that dbinom x, sze prob) gives the *value* of the binomial distribution, i e lecture notation. the a) Write code to compute the sum of the values of the binomial pl(x) for all integer x's between 0 and 2. Keep focusing on n-10, pi-0.3. Hopefully, your answer will be close to what qbinomO gave us above, because the sum of the "heights" of p(x) is supposed to be the area under p(x). (For technical reasons that we may discuss later, the answers may not be exactly the same; but they should be close.)
Please solve on only PART 2 b) and c) , PART 1 is only for REFERENCE :)

Answer 1

(b) We use the rbinom function to draw a sample of size 100 from the binomial distribution p(x) and then calculate mean and variance in the following way:
a = rbinom(100, 10, 0.3)
mean(a)
var(a)

(c) We compute the 2 graphs in the following way:
x1 = x2 = y = numeric(50)
for(i in 1:50)
{
   y[i] = i^2
   x1[i] = mean(rbinom(y[i],10,0.3))
   x2[i] = var(rbinom(y[i],10,0.3))
}
par(mfrow=c(1,2))
plot(y,x1,type="o",main="Sample size vs Means")
plot(y,x2,type="o",main="Sample size vs Variances")