Respuesta :
Answer:
a) 1.3
b) 1.81
c) 1.345
d) Each drum is a 10-gallon drum
In terms of gallons, the probability mass function becomes
y 0 10 20 30 40
p(y) 0.4 0.2 0.2 0.1 0.1
e) 13 gallons
Step-by-step explanation:
a) The mean is given by the expected value for number of drums ordered.
Expected values is given by
E(X) = Σ xᵢpᵢ
x 0 1 2 3 4
p(x) 0.4 0.2 0.2 0.1 0.1
E(X) = (0×0.4) + (1×0.2) + (2×0.2) + (3×0.1) + (4×0.1) = 0 + 0.2 + 0.4 + 0.3 + 0.4 = 1.3
b) Variance = Var(X) = Σx²p − μ²
μ = E(X) = mean
Σx²p = (0² × 0.4) + (1² × 0.2) + (2² × 0.2) + (3² × 0.1) + (4² × 0.1) = 0 + 0.2 + 0.8 + 0.9 + 1.6 = 3.5
Var(X) = Σx²p − μ² = 3.5 - 1.3² = 1.81
c) Standard deviation = √variance = √1.81 = 1.345
d) Each drum is a 10-gallon drum
In terms of gallons, the probability mass function becomes
y 0 10 20 30 40
p(y) 0.4 0.2 0.2 0.1 0.1
e) Mean = E(Y)
E(Y) = Σ yᵢpᵢ
E(Y) = (0×0.4) + (10×0.2) + (20×0.2) + (30×0.1) + (40×0.1) = 13 gallons
