Question

8.4 Binomial and Gaussian distributions Investigate by plotting how as the number of segments N of a polymer chain is increased, the binomial end-to-end distribution becomes a Gaussian distribution. Compare the different distributions in a way analogous to Figure 8.4. Also, investigate the fractional error made by approximating the binomial distribution with the Gaussian. What conclusions do you draw?

Answer 1

Answer:-- Date:-14/05/2019 here we proof that as the sample size increase the binomila distribution tends to the Gaussian distribution i.e tends to the normal distribution. With help of the grahical representation of the binomila distribution for the fixed value of p=0.5 and draw a random sample for diffrent value of n and plot the binomial plot. here we take the sample size n- 5,10, 15, 20 and p 0.5 the plot of the distribution is given below; 8 8 10 8 8 15 10 15 20 bell shaped i.e. similar to the normal plot. all work done in R - software and code is given below;

graph<-function(n,p) x <- dbinom(0:n,size-n,prob-p) return(plot(x,names.arg 0:n ,type Txlab-"xylab "Pr(x-xi)")) n<-seq(5,20, by-5) par(mfrow-c(2,2) for(i in 1:4)X graph(n[il,0.5)