Discrete random variables: E(X) & Var(X)
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Flip to reveal answersWhat must the probabilities of a discrete random variable add up to?
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All 8 Flashcards — Discrete random variables: E(X) & Var(X)
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Question
What must the probabilities of a discrete random variable add up to?
Answer
Exactly 1 (ΣP(X=x) = 1). Use this to find any unknown probability.
Question
What is the formula for E(X) of a discrete random variable?
Answer
E(X) = Σ x·P(X=x) — each value times its probability, all added.
Question
What is the formula for E(X²)?
Answer
E(X²) = Σ x²·P(X=x) — square each value, then weight by its probability.
Question
What is the formula for Var(X) of a discrete random variable?
Answer
Var(X) = E(X²) − [E(X)]² — mean of the squares minus the square of the mean.
Question
How do you find a missing probability k in a table?
Answer
Set the sum of all probabilities equal to 1 and solve for k.
Question
X: P(X=1)=0.2, P(X=2)=0.3, P(X=3)=0.4, P(X=4)=0.1. Find E(X).
Answer
E(X) = 1(0.2)+2(0.3)+3(0.4)+4(0.1) = 2.4.
Question
Find Var(X) if E(X²)=6.6 and E(X)=2.4.
Answer
Var = 6.6 − 2.4² = 6.6 − 5.76 = 0.84.
Question
What is E(aX + b) in terms of E(X)?
Answer
E(aX + b) = a·E(X) + b. (And Var(aX + b) = a²·Var(X).)
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Continuous random variables (HL only)
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