Continuous: mean, median, mode, variance
Practice Flashcards
Flip to reveal answersWhat is the mean E(X) of a continuous random variable?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 8 Flashcards — Continuous: mean, median, mode, variance
Sign up free to track progress and get spaced-repetition review schedules.
Question
What is the mean E(X) of a continuous random variable?
Answer
E(X) = ∫ x·f(x) dx over the support (the continuous version of Σ x·P).
Question
How do you find the median m of a continuous variable?
Answer
Solve ∫ from the bottom of the support up to m of f(x) dx = 0.5 (half the area to the left).
Question
How do you find the mode of a continuous variable?
Answer
It's where f is tallest: solve f'(x) = 0 (a maximum), or read the peak off the curve.
Question
What is the variance of a continuous random variable?
Answer
Var(X) = ∫ x²·f(x) dx − [E(X)]² — mean of the squares minus the square of the mean.
Question
f(x) = (3/8)x² on [0, 2]. Find E(X).
Answer
E(X) = ∫₀² x·(3/8)x² dx = ∫₀² (3/8)x³ dx = 3/2.
Question
f(x) = (3/8)x² on [0, 2]. Find the median m.
Answer
∫₀ᵐ (3/8)x² dx = m³/8 = 0.5, so m³ = 4 and m = ∛4 ≈ 1.59.
Question
If f is monotonic (always increasing) on [a, b], where is the mode?
Answer
At the endpoint where f is largest (e.g. x = b if f is increasing) — there's no interior peak.
Question
For Y = aX + b, what are E(Y) and Var(Y)?
Answer
E(Y) = a·E(X) + b and Var(Y) = a²·Var(X).
Read the notes
Full study notes for Continuous: mean, median, mode, variance
Topic 4.14 hub
Continuous random variables (HL only)
More from Topic 4.14
All flashcards in this topic
Math AA exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free