Answer:
a) E(X) = $7.4124
b) Standard deviation = $277.1
Step-by-step explanation:
P(X=xᵢ) = pᵢ
P[X=winning the car($32000)]= 1/13320 = 0.000075
P[X=winning the gas card($175)] = 1/13320 = 0.000075
P[X=winning the shopping car($5)] = 13318/13320 = 0.99985
Expected value is given by
E(X) = Σ xᵢpᵢ
E(X) = (32000 × 0.000075) + (175 × 0.000075) + (5 × 0.99985) = $7.412375 = $7.4124
b) Standard deviation = √(variance)
But Variance = Var(X) = Σx²p − μ²
where μ = E(X) = 7.4124
Σx²p = (32000² × 0.000075) + (175² × 0.000075) + (5² × 0.99985) = 76,827.29
Var(X) = 76,827.29 - 7.4124² = 76,772.349
Standard deviation = √(76,772.349) = $277.1
