Answer:
A) $0.940
B) 0.886
C) $0.941
Step-by-step explanation:
P(X=xᵢ) = pᵢ
P[X=$1000] = 0.00002
P[X=$100] = 0.0002
P[X=$50] = 0.0009
P[X=$20] = 0.004
P[X=$5] = 0.008
P[X=$2] = 0.05
P[X=$1] = 0.11
Expected value is given by
E(X) = Σ xᵢpᵢ
But because we're finding the profit on each ticket now,
E(X) = (1 - (1000 × 0.00002))+ (1 - (100 × 0.0002))+ (1 - (50 × 0.0009))+ (1 - (20 × 0.004))+ (1 - (5 × 0.008))+ (1 - (2 × 0.05))+ (1 - (1 × 0.11)) = $6.585
On the average of per ticket = $6.585/7 = $0.940
b) Variance = sum of deviations/number of tickets
Sum of deviations = (1 - (1000 × 0.00002))² + [1 - (100 × 0.0002))² + (1 - (50 × 0.0009))² + (1 - (20 × 0.004))² + (1 - (5 × 0.008))² + (1 - (2 × 0.05))² + (1 - (1 × 0.11))² = 6.202925
Variance = 6.202925/7 = 0.886
C) Standard deviation = √(variance)
Standard deviation = √(0.8861321429) = $0.941
