Answer:
(a) E(X) = 3
(b) Var(X) = 12.1067
Explanation:
(a) E[X]
E[X]T = E[X]T=A + E[X]T=B + E[X]T=C
= (2.6 + 3 + 3.4)/3
= 2.6 (1/3) + 3(1/3) + 3.4(1/3)
= 2.6/3 + 1 + 3.4/3
= 3
(b) Var (X) = E[X²]−(E[X])²
Recall that if Y ∼ Pois(λ), then E[Y 2] = λ+λ2. This implies that
E[X²] = [(2.6 + 2.6²) + (3 + 3²) + (3.4 + 3.4²)]/3
= (9.36 + 12 + 14.96)/3
= 36.32/3
= 12.1067
Var(X) = E[X²]−(E[X])²
= 12 - 3²
= 12.1067 - 9
= 3.1067
Answer:
29,143
Explanation:
Profit target = 25% on sales
Fixed cost = $51,000
Variable cost = $9.50 per unit
Sales price per unit = $15
To achieve profit target, let the number of units sold be y
Total sales = 15y
Total variable cost = 9.5y
Profit = 0.25 × 15y
= 3.75y
Sales - Cost = profit
15y - (51000 + 9.5y) = 3.75y
15y - 9.5y - 3.75y = 51000
1.75y = 51000
y = 51000/1.75
y = 29143
29,143 bears must be sold to meet the profit goal.
Answers in the completed spreadsheet, as well as the formuals I used.
Hope this helps!
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