Question

Plot using RStudio

Consider a binomial random variable, X.

i. Plot the pmf of X ∼Bin(n = 10, p = 0.3).

ii. Plot the pmf of X ∼Bin(n = 10, p = 0.7).

iii. Plot the pmf of X ∼Bin(n = 100, p = 0.3).

iv. What happens to the shape of the pmf of X ∼Bin(n, p) when p gets larger?

v. What happens when n gets larger

Answer 1

Solution:

We are given that: X follows a Binomial distribution.

We have to plot the pmf of X for given parameters using R code.

i) Plot the pmf of X ∼Bin(n = 10, p = 0.3).

we use following R code:

x<- seq(0,10,by =1)

y<-dbinom(x,10,0.3)

plot(x,y)

Thus we get following plot:

ii. Plot the pmf of X ∼Bin(n = 10, p = 0.7).

x<- seq(0,10,by =1)

y<-dbinom(x,10,0.7)

plot(x,y)

iii. Plot the pmf of X ∼Bin(n = 100, p = 0.3).

x<- seq(0,100,by =1)

y<-dbinom(x,100,0.3)

plot(x,y)

iv. What happens to the shape of the pmf of X ∼Bin(n, p) when p gets larger?

From part i and ii, we can see as p gets larger , shape of pmf shifts from left skewed distribution to right skewed distribution.

v. What happens when n gets larger

From part iii) we can see as value of n gets larger, the shape of pmf becomes approximately Normal.