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.

1 個解答

  • 慈信
    Lv 4
    5 年前

    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)