Respuesta :
To find the mean, variance, and standard deviation for the given probability distribution, we will apply the following formulas:
1. Mean (Expected Value):
Mean (μ) = Σ(X * P(X))
Mean = (-1 * 0.553) + (6 * 0.103) + (11 * 0.22) + (10 * 0.124)
Mean = -0.553 + 0.618 + 2.42 + 1.24
Mean = 3.725
2. Variance:
Variance (σ^2) = Σ[(X - μ)^2 * P(X)]
Variance = [(-1 - 3.725)^2 * 0.553] + [(6 - 3.725)^2 * 0.103] + [(11 - 3.725)^2 * 0.22] + [(10 - 3.725)^2 * 0.124]
Variance = (4.725)^2 * 0.553 + (2.275)^2 * 0.103 + (7.275)^2 * 0.22 + (6.275)^2 * 0.124
Variance = 22.296975 + 0.532275 + 11.974475 + 4.76215
Variance = 39.565875
3. Standard Deviation:
Standard Deviation (σ) = √Variance
Standard Deviation = √39.565875
Standard Deviation ≈ 6.293
Therefore:
A. Mean = 3.725
B. Variance = 39.566
C. Standard Deviation ≈ 6.293
simpler terms:
A. Mean = 3.725
This means that if you were to pick a random number from the list (-1, 6, 11, 10) based on the given probabilities, the average (mean) number you would expect to get is approximately 3.725.
B. Variance = 39.566
Variance tells us how spread out the numbers are from the average. The variance of 39.566 indicates that the numbers in the list (-1, 6, 11, 10) are spread out quite a bit from the average value of 3.725.
C. Standard Deviation ≈ 6.293
The standard deviation is a measure of how much the numbers vary or deviate from the mean. A standard deviation of approximately 6.293 tells us that the numbers in the list (-1, 6, 11, 10) vary by about 6.293 units from the mean value of 3.725
hope this helps
