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 ${\displaystyle 1}$.

${\displaystyle 0.29}$ is between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive, which meets the first property of the probability distribution.

${\displaystyle 0.45}$ is between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive, which meets the first property of the probability distribution.

${\displaystyle 0.12}$ is between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive, which meets the first property of the probability distribution.

${\displaystyle 0.14}$ 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 ${\displaystyle 0.29+0.45+0.12+0.14=1}$.

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 ${\displaystyle 0.29}$ by ${\displaystyle 1}$.

Multiply ${\displaystyle 2}$ by ${\displaystyle 0.45}$.

Multiply ${\displaystyle 3}$ by ${\displaystyle 0.12}$.

Multiply ${\displaystyle 4}$ by ${\displaystyle 0.14}$.

Add ${\displaystyle 0.29}$ and ${\displaystyle 0.9}$.

Add ${\displaystyle 1.19}$ and ${\displaystyle 0.36}$.

Add ${\displaystyle 1.55}$ and ${\displaystyle 0.56}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 2.11}$.

Subtract ${\displaystyle 2.11}$ from ${\displaystyle 1}$.

Raise ${\displaystyle -1.11}$ to the power of ${\displaystyle 2}$.

Multiply ${\displaystyle 1.2321}$ by ${\displaystyle 0.29}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 2.11}$.

Subtract ${\displaystyle 2.11}$ from ${\displaystyle 2}$.

Raise ${\displaystyle -0.11}$ to the power of ${\displaystyle 2}$.

Multiply ${\displaystyle 0.0121}$ by ${\displaystyle 0.45}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 2.11}$.

Subtract ${\displaystyle 2.11}$ from ${\displaystyle 3}$.

Raise ${\displaystyle 0.89}$ to the power of ${\displaystyle 2}$.

Multiply ${\displaystyle 0.7921}$ by ${\displaystyle 0.12}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 2.11}$.

Subtract ${\displaystyle 2.11}$ from ${\displaystyle 4}$.

Raise ${\displaystyle 1.89}$ to the power of ${\displaystyle 2}$.

Multiply ${\displaystyle 3.5721}$ by ${\displaystyle 0.14}$.

Add ${\displaystyle 0.357309}$ and ${\displaystyle 0.005445}$.

Add ${\displaystyle 0.362754}$ and ${\displaystyle 0.095052}$.

Add ${\displaystyle 0.457806}$ and ${\displaystyle 0.500094}$.