Question

How do you do these questions?

Answer 1

μ ≈ 2.33

σ ≈ 1.25

Explanation:

Each person has equal probability of ⅓.

`\left[\begin{array}{cc}X&P(X)\\1&(1)/(3)\\2&(1)/(3)\\4&(1)/(3)\end{array}\right]`

The mean is the expected value:

μ = E(X) = ∑ X P(X)

μ = (1) (⅓) + (2) (⅓) + (4) (⅓)

μ = ⁷/₃

The standard deviation is:

σ² = ∑ (X−μ)² P(X)

σ² = (1 − ⁷/₃)² (⅓) + (2 − ⁷/₃)² (⅓) + (4 − ⁷/₃)² (⅓)

σ² = ¹⁴/₉

σ ≈ 1.25