Question

This project requires writing computer code to generate random variables of various kinds and measure their probability distributions. 1. Generate a sequence of each of the following types of random variables, each sequence should be at least 10,000 points long.

(a) A binomial random variable. Let the number of Bernoulli trials ben 12. Recall that the binomial random variable is defined as the number of 1's in n trials for a Bernoulli (binary) random variable. Let the parameter p in the Bernoulli trials be p 0.5109.

(b) A Poisson random variable as a limiting case of the binomial random variable with p 0.0125 or less and n 80 or more while maintaining a np 1

(c) A type 1 geometric random variable with parameter p 0.09

(d) A (continuous uniform random variable in the range [-2, 5]

(e) A Gaussian random variable with mean u 1.3172 and variance 1.9236. (f An exponential random variable with parameter 1.37

Answer 1

See explaination for details

Explanation:

a.

Here n = 12 and p = 0.5109

steps :

Calc --> Random data --> Binomial --> Number of rows of data to generate : 10000 --> Store in columns(s) : C1

--> Number of trials : 12 --> Probability of success : 0.5109 --> ok

This will generate the size of 10,000 from Binomial distribution.

b. The Poisson(µ) distribution is the limit of the binomial(n, p) distribution with µ = np as n ? ?.

n = 80, p = 0.0125

Here µ = 80*0.0125 = 1

Calc --> Random data --> Poisson --> Number of rows of data to generate : 10000 --> Store in columns(s) : C2

--> mean : 1 --> ok

This will create sample of 10,000 from Poisson distribution.

d. Calc --> Random data --> Uniform --> Number of rows of data to generate : 10000 --> Store in columns(s) : C3

-->Lower endpoint : -2 --> Upper endpoint : 5 --> ok

This will create random sample of size 10,000 from Uniform distribution.

e. Variance = 1.9236

sd = sqrt(1.9236) = 1.387

Calc --> Random data --> Normal --> Number of rows of data to generate : 10000 --> Store in columns(s) : C4

-->Mean : 1.3172 --> standard deviation : 1.387 --> ok

This will generate random sample of size 10000 from Normal distribution.

f. Calc --> Random data --> exponential --> Number of rows of data to generate : 10000 --> Store in columns(s) : C5 -->Scale : 1.37 --> Threshold : 0 --> ok

This will generate random sample of size 10,000 from Exponential distribution.