- Mean (First Raw Moment) / Average (𝜇 or 𝑋̅)
- is a type of Central Tendency
- is the sum of all values divided by the total number of values
- is the balance point of a distribution
- Expected Value / Expectation (𝐄[])
- a predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence
- is a property of a variable (either random or not random)
- calculating expectation of continuous distribution & discrete distribution
Syntax
When “E” is used to denote “expected value”, authors use a variety of stylizations:
- the expectation operator can be stylized as 𝐄 (bold upright), 𝐸 (italic), or 𝔼 (blackboard bold)
- the expectation of 𝑋 can be stylized as 𝐸(𝑋), 𝐸[𝑋], 𝐸𝑋, 𝜇𝑋, whereas ⟨𝑋⟩, ⟨𝑋⟩𝑎𝑣, and 𝑋̅ are commonly used in physics, and 𝑀(𝑋) in Russian-language literature.