The formula to calculate the expected value for a set of discrete outcomes is:
\[ E = \sum (P_i \times X_i) \]
Where:
The expected value, also known as the mean or average, is a measure of the center of a probability distribution. For a set of discrete outcomes, the expected value is calculated by multiplying each outcome by its probability and summing these products. This gives a weighted average that reflects the likelihood of each outcome occurring. The expected value is a fundamental concept in probability and statistics, used in various fields such as finance, economics, and decision theory.
Let's assume the following values:
Step 1: Multiply each outcome by its probability:
\[ 1 \times 0.2 = 0.2 \]
\[ 2 \times 0.5 = 1 \]
\[ 3 \times 0.3 = 0.9 \]
Step 2: Sum all the products:
\[ 0.2 + 1 + 0.9 = 2.1 \]
The Expected Value (E) is 2.1.
