IAI Actuarial Core Principles · Actuarial Statistics · Expectations and conditional expectations
X is uniform on (0, 6). What is E[X²]?
E[X²] equals 12. For a uniform variable on (0, 6), the variance is 3 and the mean is 3, so the second moment is 3 + 9 = 12.
- A9
- B12Correct
- C3
- D18
- 36
Explanation
E[X²] = ∫0^6 x²/6 dx = 6²/3 = 12. Alternatively Var = 36/12 = 3 and mean² = 9, summing to 12. Option 9 is mean squared only; 3 is the variance only.
Did you get it right without looking?
One question tells you little. A timed set on Expectations and conditional expectations shows your real accuracy, how long you take and where you lose marks.
More Expectations and conditional expectations questions
- Let X be uniform on (0, 10) and let Y = min(X, 4), representing a claim capped at Rs 4 lakh. What is E[Y]?
- A claim amount X (in rupees thousand) has density f(x) = 2/x^3 for x > 1 and 0 otherwise. What is E[X]?
- Given Λ, X is Poisson with mean Λ. Λ has mean 3 and variance 2. What is Var(X)?
- The joint probability function of X and Y is P(X=0,Y=0)=0.2, P(X=0,Y=1)=0.1, P(X=1,Y=0)=0.3, P(X=1,Y=1)=0.4. What is E[X | Y = 1]?
- X and Y satisfy E[Y|X] = 2 + 3X. X has mean 4 and variance 5. Var(Y|X) = 10 for all X. What is Var(Y)?
- Given Λ, a risk has claim count N with Poisson distribution of mean Λ. Λ takes value 2 with probability 0.5 and value 6 with probability 0.5…