Question

Write it in P program. This is only one question with multiple parts, so please answer all the parts of the question, it is not much. Please also include a screenshot of your R program.

1. Generator 500 random numbers from the Binomial distribution with size=100, p=0.5 (define it X).
2. Standardize the vector X using the following equation (define it Z):

Z=(X-E(X))/sd(X)

Where E(X)= mean of B(n,p), which is np, sd(X) = standard deviation of B(n,p), which is sqrt(np(1-p)).

3. Make a histogram of Z and discuss the shape of the histogram.
4. Convince your answer from 3 using the method we have learned in the class.
5. Do the same thing for (n, p) = (100, 0.1), (100, 0.3), (100, 0.7), (100, 0.9), and draw 4 histograms of Z, and discuss about the shape of the histogram.

Answer 1

To generate 500 random numbers from Binomial distribution n=100, we can use rbinom(500,100,0.5) p=0.5 in R.

Single histogram is for B(100,0.5) which seems to be symmetric about 0.

Histogram B(100,0.1) shows that distribution is right skewed.

Histogram B(100,0.3) shows almost symmetric about with a little positive skewness.

Histogram B(100,0.7) almost symmetric but little left skewed.

Histogram B(100,.9) is left skewed.