Curriculum
Statistics — Third Secondary
Unit 1: Correlation and Regression
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Unit 2: Advanced Statistical Measures
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Unit 3: Probability
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Unit 4: Random Variables
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Unit 5: The Normal Distribution
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Text lesson
Expectation and Variance
Expectation and Variance
Properties of expectation and variance
Properties of expectation and variance
- If Y = aX + b
- where a and b are fixed numbers
- then:
- E(aX + b) = a E(X) + b. The expectation changes in the same way as the values.
- Var(aX + b) = a² Var(X). Adding the constant b does not change the variance.
- The standard deviation of Y is σY = |a| × σX.
- These properties help us find the expectation and variance of a new variable built from a known one, without rewriting the whole distribution.
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