Finite Mathematics

Finite Mathematics covers mathematical concepts and techniques applicable to business and social sciences, including matrix algebra, linear programming, and probability.

Advanced Topics

Advanced Probability: Expected Value and Variance

Digging Deeper: Expected Value and Variance

Expected value tells us the average result we can expect from a random event over many trials. Variance measures how spread out the possible results are.

Calculating Expected Value

The expected value (\(E[X]\)) of a random variable \(X\) is:

\[ E[X] = \sum (x_i \times p_i) \]

where \(x_i\) is a possible outcome, and \(p_i\) is its probability.

Why Variance Matters

Variance lets us know how much risk or variability is involved. High variance means outcomes can be very different from the average!

Where It's Used

This knowledge is essential in finance, insurance, and any decision-making under uncertainty.

Key Formula

\[E[X] = \sum (x_i \times p_i)\]

Examples

  • Calculating the average winnings in a lottery game.

  • Determining how risky an investment is by measuring variance.

In a Nutshell

Expected value shows the likely outcome; variance tells us about the risk involved.