Discrete Expected Value Visualization

Expected Value of Discrete Distribution

Formula: E[X] = Σ x · P(X = x)

Expected Value: 3.400

Adjust Probabilities:

P(X = 1)

0.100

Contribution: 0.100

P(X = 2)

0.150

Contribution: 0.300

P(X = 3)

0.250

Contribution: 0.750

P(X = 4)

0.300

Contribution: 1.200

P(X = 5)

0.150

Contribution: 0.750

P(X = 6)

0.050

Contribution: 0.300

Understanding Expected Value:

The expected value is the weighted average of all possible values, where each value is weighted by its probability. The red dashed line shows where the expected value falls on the x-axis.

Each bar shows the probability of that outcome, and the number inside shows that value's contribution to the expected value (x · P(X = x)).

Discrete Random Variables

Calculation Formula

Interpretation

Understanding Discrete Expected Value

For a discrete random variable X with outcomes x₁, x₂, ..., xₙ and corresponding probabilities p₁, p₂, ..., pₙ, the expected value is E[X] = Σ xᵢ · pᵢ. This represents the long-run average value if the experiment were repeated many times.

Discrete Random Variables

Discrete random variables have countable outcomes. Examples include dice rolls, coin flips, number of customers, or any scenario with distinct, separate possible values.

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Calculation Formula

Expected value for discrete variables is calculated by multiplying each outcome by its probability and summing all these products: E[X] = x₁p₁ + x₂p₂ + ... + xₙpₙ.

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Interpretation

The expected value is the theoretical mean if you could repeat the random process infinitely. It may not be an actual possible outcome of the random variable itself.

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