How to find the mean median standard deviation of a discrete random variable

The formula for the mean is:

2. Median

The median of a discrete random variable is the smallest value $x_k$ such that the cumulative probability $P(X \le x_k)$ is greater than or equal to 0.5.

This $x_k$ is the median.

3. Standard Deviation

The standard deviation measures the spread or dispersion of the values around the mean. It is the square root of the variance.

There are two common formulas: * Using the definition: $Var(X) = \sum_{i} (x_i - \mu)^2 P(X=x_i)$ For each value $x_i$, subtract the mean $\mu$, square the result, and multiply by its probability $P(X=x_i)$. Sum these values. * Using the computational formula (often easier): $Var(X) = E(X^2) - (E(X))^2$ First, calculate $E(X^2) = \sum_{i} x_i^2 P(X=x_i)$. This means squaring each $x_i$, multiplying by its probability, and summing. Then, subtract the square of the mean $(E(X))^2$.