Question

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

Answer 1

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

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

$a=0, b=9$

The probability density function is

$$f(x)=\frac{1}{9-0}$$

for $0 \leq x \leq 9.$

Formulas for the theoretical mean and standard deviation are

$$\mu=\dfrac{0+9}2=4.5,\sigma=\sqrt{\dfrac{(9-0)^2}{12}}=0.25$$