Question

Generate 200 random numbers using each of the following continuous distributions and plot the histograms

(a) Uniform (use A = 3 and B = 7)

(b) Exponential (use population mean = 0.2)

(c) Gamma (use parameters 3 and 2)

(d) Normal (use µ = 2 and σ = 5)

Attach the histogram plots and reflect on what you observe. Hint: Use RAND() to generate uniform random numbers and use inverse CDF to generate random numbers for each distribution.

Answer 1

Table is generated using Excel formula

For Uniform distribution : Rand()*(B-A) + A

For Exponential distribution : -1*Average(Rand()) * ln(1-rand())

For Gamma distribution : Gamma.inv(rand(),alpha,beta)

For normal distribution : norm.inv(rand(),mean,sd)

a) Histogram of a uniform distribution :

b) Histogram of a exponential distribution :

c) Histogram of a Gamma distribution :

d) Histogram of a normal distribution :

Data table was deleted due to answer size limits : data was generated using the above formulas in excel