A Statistics Problem?
Assume that Y is normally distributed with mean mu and standard
deviation sigma. After observing a value of Y, a mathematician constructs
a rectangle with length L = |Y| and width W = 6|Y|. Let A
denote the area of the resulting rectangle. What is E(A)?
Could you please show me the steps as well? I really want to learn. Thanks.
- 慈信Lv 45 年前最愛解答
L = |Y| , W = 6|Y|
A = L * W = |Y| * 6|Y| = 6Y²
σ² = E(Y²) - μ²
E(Y²) = σ² + μ²
E(A) = E(6Y²) = 6E(Y²) = 6(σ² + μ²)