Suppose there are 5 men and 6 women at a party. The task of going to the store for more food and drinks is assigned to 2 party guests, chosen at random. Let W denote the number of women selected. Find E[W] and E[W2 ].

E (W) = 1.0909; E (W²) = 1.6362

Step-by-step explanation:

total number of guests = 5men + 6women = 11

number if ways 2 guests are selected from 11 guests = ¹¹C₂ = 55

Case 1: When no women is selected

P (W=0) = (⁶C₀. ⁵C₂) / 55 = 0.1818

W*PW = 0

W²*PW = 0

Case 2: When 1 women is selected

P (W=1) = (⁶C₁. ⁵C₁) / 55 = 0.5455

W*PW = 0.5455

W²*PW = 0.5454

Case 3: When 2 women are selected

P (W=2) = (⁶C₂. ⁵C₀) / 55 = 0.2727

W*PW = 0.5454

W²*PW = 1.0908

∑W*PW = 1.0909 = E (W)

∑W²*PW = 1.6362 = E (W²)