Answer:
Mean = 3
Variance = 2
Step-by-step explanation:
Since number of eggs he eats is equally likely to any 5 numbers, probability of each one will be (1/5) = 0.2
The probability mass function will therefore be
x 1 2 3 4 5
p 0.2 0.2 0.2 0.2 0.2
The mean is given as the expected value
And expected value is given as
E(X) = Σ xᵢpᵢ
where x = each possible sample space
p = probability of the sample space occurring.
E(X) = (1×0.2) + (2×0.2) + (3×0.2) + (4×0.2) + (5×0.2) = 3 eggs.
b) Variance is given by
Variance = Var(X) = Σx²p − μ²
where μ = E(X)
Σx²p = (1² × 0.2) + (2² × 0.2) + (3² × 0.2) + (4² × 0.2) + (5² × 0.2) = 0.2 + 0.8 + 1.8 + 3.2 + 5 = 11
Var(X) = Σx²p − μ² = 11 - 3² = 11 - 9 = 2
