Answer:
- The Expected value for the sum is 30.
- The Observed sum of 50 draws is 33.
- The Chance Error on the 50 draws is 3.
- The Standard Error on 50 draws is 2.191.
Step-by-step explanation:
The box contains [0, 0, 1, 1, 1]
Using probability to predict the expected outcome.
On one draw, the probability of drawing a 0 is (2/5).
And the probability of drawing a 1 is (3/5).
Probability mass function would look like
X | P(X)
0 | 0.40
1 | 0.60
So, expected value on one draw would be
E(X) = Σ xᵢpᵢ
xᵢ = each variable
pᵢ = probability of each variable
E(X) = (0×0.40) + (1×0.60) = 0.60.
Standard error on one draw = √[Σ(xᵢ - μ)²/N]
μ = E(X) = 0.60
Σ(xᵢ - μ)² = (0 - 0.60)² + (0 - 0.60)² + (1 - 0.6)² + (1 - 0.6)² + (1 - 0.6)² = 1.20
SE = √(1.2/5) = 0.490
So, for 50 draws (with replacement),
E(50X) = 50E(X) = 50 × 0.60 = 30.
For 50 draws, standard error = √50 × 0.490 = 2.191
The expected value for the sum = 30
The observed valued for the sum = (33×1) + (17×0) = 33
Chance Error = (Observed Outcome) - (Expected Outcome) = 33 - 30 = 3
Standard error gives an idea of how large the chance error would be.
Standard error on 50 draws = 2.191
Hope this Helps!!!
