IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions
A random sample of n = 4 observations is drawn from a Uniform(0, 1) distribution. What is the expected value of the sample maximum X(4)?
The expected maximum of four Uniform(0,1) observations is 0.80, because the k-th order statistic has mean k/(n+1), which for k = 4 and n = 4 equals 4/5. The value 0.20 would be the expected minimum instead.
- A0.50
- B0.60
- C0.75
- D0.80Correct
- 0.20
Explanation
For a Uniform(0,1) sample of size n, E[X(k)] = k/(n+1). With k = n = 4 this gives 4/5 = 0.80. The value 0.20 is the expectation of the minimum, and 0.60 uses k/n... for k=3 over 5, not the maximum.
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