Expected Value, Variance & Standard Deviation (Grade 12)
Free printable Grade 12 Mathematical Methods worksheet on the expected value, variance and standard deviation of a discrete random variable. Answers computed by definitional summation.
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Grade 12 · Math worksheet
Name
Date
Math
Probability Distributions: Expected Value, Variance & Standard Deviation
For each discrete random variable, find the expected value E(X), the variance Var(X) = E(X^2) - [E(X)]^2, or the standard deviation. Round variance and standard deviation to 3 decimal places.
- 1.A discrete random variable X has this probability distribution: P(X=0)=0.2, P(X=3)=0.2, P(X=4)=0.1, P(X=6)=0.2, P(X=9)=0.3. Find the expected value E(X).
- 2.A discrete random variable X has this probability distribution: P(X=3)=0.4, P(X=5)=0.2, P(X=7)=0.1, P(X=8)=0.3. Find the variance Var(X). Round to 3 decimal places.
- 3.A discrete random variable X has this probability distribution: P(X=1)=0.5, P(X=3)=0.1, P(X=9)=0.4. Find the expected value E(X).
- 4.A discrete random variable X has this probability distribution: P(X=0)=0.35, P(X=1)=0.2, P(X=4)=0.15, P(X=8)=0.15, P(X=9)=0.15. Find the variance Var(X). Round to 3 decimal places.
- 5.A discrete random variable X has this probability distribution: P(X=1)=0.35, P(X=3)=0.4, P(X=8)=0.25. Find the expected value E(X).
- 6.A discrete random variable X has this probability distribution: P(X=4)=0.25, P(X=6)=0.35, P(X=7)=0.4. Find the variance Var(X). Round to 3 decimal places.
- 7.A discrete random variable X has this probability distribution: P(X=2)=0.25, P(X=4)=0.5, P(X=6)=0.25. Find the standard deviation of X. Round to 3 decimal places.
- 8.A discrete random variable X has this probability distribution: P(X=0)=0.3, P(X=1)=0.2, P(X=7)=0.5. Find the variance Var(X). Round to 3 decimal places.
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