Answer:
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)
Answer:
E(W)= ∑WP(W)=1.0909
E(W^{2})= ∑W^{2}P(W)=1.6363
Step-by-step explanation:
Here W can take value 0, 1, 2. There are total 5+6= 11 guests in the party. So total number of ways of selecting 2 guests out of 11 is
\binom{11}{2}=55
For W = 0 means both selected guests are men. So
P(W=0)=\frac{\binom{5}{2}}{55}=\frac{10}{55}=0.1818
For W = 1 means one man and one woman selected. So
P(W=1)=\frac{\binom{5}{1}\binom{6}{1}}{55}=\frac{30}{55}=0.5455
For W = 2 means two women selected. So
P(W=2)=\frac{\binom{6}{2}}{55}=\frac{15}{55}=0.2727
Following table shows the calcualtion for E(W) and E(W^2):
W P(W) W*P(W) W^2*P(W)
0 0.1818 0 0
1 0.5455 0.5455 0.5455
2 0.2727 0.5454 1.0908
Total 1 1.0909 1.6363
So
E(W)= ∑WP(W)=1.0909
E(W^{2})= ∑W^{2}P(W)=1.6363
