Exercise · ZW-VARIANCE-003 · ★★☆ Intermediate
\(X\) has density \(f(x)=2x\) on \([0,1]\). Compute \(\operatorname{Var}(X)\).
Choose one option.
Show answer
- A. \(\dfrac{1}{18}\)
Explanation
\(E[X]=\tfrac23\), \(E[X^2]=\tfrac12\), hence \(\operatorname{Var}(X)=\tfrac12-\tfrac49=\tfrac1{18}\).
Review the concept: Variance
The variance \(\operatorname{Var}(X)\) of a random variable \(X\) measures how spread out its values are around its expectation \(E\): it is the expected value of the squared deviation.
\[\operatorname{Var}(X)=E\big[(X-E[X])^2\big]\]
More practice problems: variance
- ZW-VARIANCE-001 X takes the values 0, 1 and 2 with probabilities 0.2, 0.5 and 0.3 (so E[X]=1.1). Compute Var(X).
- ZW-VARIANCE-002 Compute the variance of the outcome of a fair die.
- ZW-VARIANCE-004 If Var(X)=4, what is Var(3X+1)?
- ZW-VARIANCE-005 If E[X]=2 and E[X^2]=7, what is Var(X)?
- ZW-VARIANCE-006 X equals 1 with probability 0.3 and 0 with probability 0.7. Compute Var(X).
- ZW-VARIANCE-007 Which statement about the variance is correct?
- ZW-VARIANCE-008 X equals -2 or 2 with probability tfrac12 each. Compute Var(X).
- ZW-VARIANCE-009 If Var(X)=5, what is Var(-2X)?