Answer to Question #289708 in Statistics and Probability for Paula

Question

 Identify the appropriate distribution function if we want to select 20 random numbers between 0 and 9.

Answer 1

Solution:

Uniform Distribution is appropriate distribution.

The random-number generator on calculators randomly generates a number between 0 and 9. The random variable X, the number generated, follows a uniform probability distribution.

The notation for the uniform distribution is $X{\sim} U(a, b)$ where a= the lowest value of x and b= the highest value of x.

The probability density function is

$f(x)=\frac{1}{b-a}$

for $a \leq x \leq b.$

Formulas for the theoretical mean and standard deviation are

$\mu=\dfrac{a+b}2,\sigma=\sqrt{\dfrac{(b-a)^2}{12}}$