Statistics Examples

A discrete random variable ${\displaystyle x}$ takes a set of separate values (such as ${\displaystyle 0}$, ${\displaystyle 1}$, ${\displaystyle 2}$...). Its probability distribution assigns a probability ${\displaystyle P\left(x\right)}$ to each possible value ${\displaystyle x}$. For each ${\displaystyle x}$, the probability ${\displaystyle P\left(x\right)}$ falls between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive and the sum of the probabilities for all the possible ${\displaystyle x}$ values equals to ${\displaystyle 1}$.

${\displaystyle 0.2}$ is between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive, which meets the first property of the probability distribution.

${\displaystyle 0.4}$ is between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive, which meets the first property of the probability distribution.

For each ${\displaystyle x}$, the probability ${\displaystyle P\left(x\right)}$ falls between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive, which meets the first property of the probability distribution.

Find the sum of the probabilities for all the possible ${\displaystyle x}$ values.

The sum of the probabilities for all the possible ${\displaystyle x}$ values is ${\displaystyle 0.2+0.4+0.4=1}$.

For each ${\displaystyle x}$, the probability of ${\displaystyle P\left(x\right)}$ falls between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive. In addition, the sum of the probabilities for all the possible ${\displaystyle x}$ equals ${\displaystyle 1}$, which means that the table satisfies the two properties of a probability distribution.

Multiply ${\displaystyle 4}$ by ${\displaystyle 0.2}$.

Multiply ${\displaystyle 7}$ by ${\displaystyle 0.4}$.

Multiply ${\displaystyle 11}$ by ${\displaystyle 0.4}$.

Add ${\displaystyle 0.8}$ and ${\displaystyle 2.8}$.

Add ${\displaystyle 3.6}$ and ${\displaystyle 4.4}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 8}$.

Subtract ${\displaystyle 8}$ from ${\displaystyle 4}$.

Raise ${\displaystyle -4}$ to the power of ${\displaystyle 2}$.

Multiply ${\displaystyle 16}$ by ${\displaystyle 0.2}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 8}$.

Subtract ${\displaystyle 8}$ from ${\displaystyle 7}$.

Raise ${\displaystyle -1}$ to the power of ${\displaystyle 2}$.

Multiply ${\displaystyle 0.4}$ by ${\displaystyle 1}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 8}$.

Subtract ${\displaystyle 8}$ from ${\displaystyle 11}$.

Raise ${\displaystyle 3}$ to the power of ${\displaystyle 2}$.

Multiply ${\displaystyle 9}$ by ${\displaystyle 0.4}$.

Add ${\displaystyle 3.2}$ and ${\displaystyle 0.4}$.

Add ${\displaystyle 3.6}$ and ${\displaystyle 3.6}$.