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 ${\displaystyle 1}$.

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

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

${\displaystyle 0.1}$ 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 ${\displaystyle 0.4+0.2+0.1+0.1+0.1+0.1=1}$.

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 ${\displaystyle 0.4}$.

Multiply ${\displaystyle 7}$ by ${\displaystyle 0.2}$.

Multiply ${\displaystyle 9}$ by ${\displaystyle 0.1}$.

Multiply ${\displaystyle 11}$ by ${\displaystyle 0.1}$.

Multiply ${\displaystyle 13}$ by ${\displaystyle 0.1}$.

Multiply ${\displaystyle 17}$ by ${\displaystyle 0.1}$.

Add ${\displaystyle 1.6}$ and ${\displaystyle 1.4}$.

Add ${\displaystyle 3}$ and ${\displaystyle 0.9}$.

Add ${\displaystyle 3.9}$ and ${\displaystyle 1.1}$.

Add ${\displaystyle 5}$ and ${\displaystyle 1.3}$.

Add ${\displaystyle 6.3}$ and ${\displaystyle 1.7}$.

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 ${\displaystyle 0.4}$.

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

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

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

Multiply ${\displaystyle 0.2}$ by ${\displaystyle 1}$.

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

Subtract ${\displaystyle 8}$ from ${\displaystyle 9}$.

One to any power is one.

Multiply ${\displaystyle 0.1}$ 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 ${\displaystyle 0.1}$.

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

Subtract ${\displaystyle 8}$ from ${\displaystyle 13}$.

Raise ${\displaystyle 5}$ to the power of ${\displaystyle 2}$.

Multiply ${\displaystyle 25}$ by ${\displaystyle 0.1}$.

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

Subtract ${\displaystyle 8}$ from ${\displaystyle 17}$.

Raise ${\displaystyle 9}$ to the power of ${\displaystyle 2}$.

Multiply ${\displaystyle 81}$ by ${\displaystyle 0.1}$.

Add ${\displaystyle 6.4}$ and ${\displaystyle 0.2}$.

Add ${\displaystyle 6.6}$ and ${\displaystyle 0.1}$.

Add ${\displaystyle 6.7}$ and ${\displaystyle 0.9}$.

Add ${\displaystyle 7.6}$ and ${\displaystyle 2.5}$.

Add ${\displaystyle 10.1}$ and ${\displaystyle 8.1}$.