Stat 992 Assignment – Presentation Day 1 - MATLAB
Question 1. Adapt the Matlab program in Code 6.2 to illustrate the Beta (α, β)
distribution where α = 2 and β = 3.
Question 2: Adapt the matlab program in Code 6.2 to illustrate the Binomial (N, θ)
distribution where N = 10 and θ = 0.7.
Question 3: Write a demonstration program to sample 10 values from a Bernoulli(θ)
distribution with θ = 0.3. Recall that there are only two possible outcomes, 0 and 1. With
probability θ, the outcome is 1, and with probability 1 − θ, the outcome is 0. In other
words, p(X = 1) = θ, and p(X = 0) = 1 − θ. In Matlab, you can simulate the Bernoulli
distribution using the binomial distribution with N = 1. However, for the purpose of this
exercise, please write the code needed to randomly sample Bernoulli distributed values
that does not make use of the built-in binomial distribution. Using a seed of 21, verify
that the first four observations agree with 1, 1, 0 and 1 respectively. Your MATLAB code
could use the following line for the seeding:
>>
seed=21; rand(’state’,seed); randn(’state’,seed);
Question 4:
In this exercise, we want to generate the random variable x=(x1, x2) from
Beta(1, 𝛽) by inverse transform method.
a)
Write down the algorithm for generating x.
b)
Use MATLAB to construct two sets of N=1000 observations each from Beta (1,4).
Set seed =131. Plot histograms of both sets on the same graph and print out the first 5
observations from each set. Observe that the first observations are x1=0.0251 and x2 =
0.0348.
c)
Find the mean of each set generated.