R

Question 1

sessionInfo()

Answer 1

provides information about the operating system, version of R and version of all R packages being used.

Question 2

How to simulate a random sample for a discrete uniform distribution

Answer 2

To generate a vector for sample space S = {1, 2, 3, ….. , 20}: S = 1:20
To simulate 100 values from this sample space: sample(S, 100, replace = TRUE)

Question 3

distribution functions

Answer 3

The R code for simulating values and calculating probabilities and quantiles from the binomial distribution uses the R functions rbinom, dbinom, pbinom and qbinom. The prefixes r, d, p, and q stand for random generation, density, distribution and quantile functions respectively. (A discrete distribution has a probability mass function rather than a density, but the prefix d is still used.)

Question 4

Random sample of 100 values from a discrete uniform distribution (1,20)

Answer 4

S=1:20
P=sample(S,100,replace=TRUE)

Question 5

a) Get a random sample of 100 values from the Bin(20,0.3)
b) Calc P(X=2)

Answer 5

a) ```
n=20
p=0.3
rbinom(100,n,p)
~~~

b) dbinom(2,n,p)

Question 6

Setting a seed

Answer 6

set.seed(n)

Question 7

Graphs

Answer 7

hist
curve

Question 8

Constructing 95% CI for the mean with unknown variance

Answer 8

The R function for a symmetrical 95% confidence interval for the mean with unknown variance is:

t.test(<sample data>, conf=0.95)

For small samples from a non-normal distribution, confidence intervals can be constructed empirically in R using the bootstrap method . For example, a non-parametric 95% confidence interval for the mean could be obtained by:
quantile(replicate(1000,mean(sample(<sample data>,replace=TRUE))), probs=c(0.025,0.975))