Respuesta :
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
xáµ¢ = each variable
páµ¢ = 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!!!
The answer of the blanks are :
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.
Probability
The box contains [0, 0, 1, 1, 1]
Using probability to predict the expected outcome.
The probability of drawing a 0 is (2/5).
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
xáµ¢ = each variable
páµ¢ = 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
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 on 50 draws = 2.191
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