Finite Math 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 ${\displaystyle 1}$.

${\displaystyle 0.3}$ 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 ${\displaystyle 0.3+0.3+0.4=1}$.

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 ${\displaystyle 0}$ by ${\displaystyle 0.3}$.

Multiply ${\displaystyle 3}$ by ${\displaystyle 0.3}$.

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

Add ${\displaystyle 0}$ and ${\displaystyle 0.9}$.

Add ${\displaystyle 0.9}$ and ${\displaystyle 2.8}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 3.7}$.

Subtract ${\displaystyle 3.7}$ from ${\displaystyle 0}$.

Raise ${\displaystyle -3.7}$ to the power of ${\displaystyle 2}$.

Multiply ${\displaystyle 13.69}$ by ${\displaystyle 0.3}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 3.7}$.

Subtract ${\displaystyle 3.7}$ from ${\displaystyle 3}$.

Raise ${\displaystyle -0.7}$ to the power of ${\displaystyle 2}$.

Multiply ${\displaystyle 0.49}$ by ${\displaystyle 0.3}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 3.7}$.

Subtract ${\displaystyle 3.7}$ from ${\displaystyle 7}$.

Raise ${\displaystyle 3.3}$ to the power of ${\displaystyle 2}$.

Multiply ${\displaystyle 10.89}$ by ${\displaystyle 0.4}$.

Add ${\displaystyle 4.107}$ and ${\displaystyle 0.147}$.

Add ${\displaystyle 4.254}$ and ${\displaystyle 4.356}$.