Question

Suppose we need to construct a random variable X = {x₁, x₂, x₃, x₄} where x₁ is sampled from N(0,1), x₂ is sampled from U(0,1), x₃ is sampled from Pois (0.5) and x₄ from B (1000,0.5) where 1000 tosses of a fair coin are taken into an account (0 = tail, 1=head). What type of samples we would expect for X? Write 10 samples.

Answer 1

We can expect a multivariate sample with 4 variates.

1st coming from standard normal, 2nd from uniform (0,1), 3rd from poisson with mean 0.5 and 4th from binomial(1000,0.5).

R Code:

normal = rnorm(n = 10,mean = 0,sd = 1)
poisson = rpois(n = 10,lambda = 0.5)
uniform = runif(n = 10, min = 0,max = 1)
binomial = rbinom(n = 10, size = 1000, prob = 0.5)
sample = cbind(normal, poisson, uniform, binomial)

Sample would be like this.

uniform - binomial normal -0.8826293 poisson 0 0.2461824 495 2 -0.2976566 1 0.1111983 515 3 1.4016976 4 1.8644216 5 -0.9210697 0 0 1 0.2046858 0.7356032 0.8534436 493 502 475 6 -0.4700412 0 0.3776223 483 0.6571153 503 7 1.18424191 8 0.85434892 9 1.0772736 0 0.7876232 0.6355296 0.9811785 503 492 510 10 -1.05134620