# Random Variables

## Discrete Random Variables

Random variables The process of drawing a sample randomly is a random experiment and any variable measured in the sample is a random variable because the values taken by the variable in the individuals of the sample are a matter of chance.

## Continuous Random Variables

Probability distribution of a continuous random variable Continuous random variables, unlike discrete random variables, can take any value in a real interval. Thus the range of a continuous random variables is infinite and uncountable.

## Problems of Discrete Random Variables

Exercise 1 Let $X$ be a discrete random variable with the following probability distribution  \begin{array}{|c|c|c|c|c|c|} \hline X & 4 & 5 & 6 & 7 & 8 \newline \hline f(x) & 0.

## Problems of Continuous Random Variables

Exercise 1 Given the continuous random variable $X$ with the following probability density function chart, Check that $f(x)$ is a probability density function. Calculate the following probabilities a. $P(X<1)$ b.