Discrete Random Variables

Discrete Random Variable

- It takes on a countable number of distinct values
- The sum of all probabilities equals to \(1\). \(\sum\limits_{\text{all}\hspace{0.5em}x}{P\left( X=x \right)}=1\)

EXAMPLES
- Number of tails obtained from \(5\)-coin tosses.
- Number of red cars passing by a road junction in \(10\) minutes.
- Average number of birds on the trees in one afternoon.
E.g.: Binomial Distribution, Poisson Distribution

Continuous Random Variable

- It takes values over a continuous range.
- Each exact value has probability \(P(X=x)=0\). For a distribution with a probability density, interval probabilities are areas under the density curve, and the total area is \(1\).

EXAMPLES
- The height of a chosen student in a school.
- The time taken to travel to school every morning.
- The weight of a loaf of bread produced in a factory.

E.g.: Normal distribution