Respuesta :
Answer:
Expected value or mean = [tex]E(x) = \mu = 7.42[/tex]
Variance = [tex]\sigma^2 = 6.283[/tex]
Standard deviation = [tex]\sigma = 2.506[/tex]
Step-by-step explanation:
We are given the following information:
x | P(x)
6 | 0.64
8 | 0.14
9 | 0.14
15 | 0.08
The expected value or mean is given by
[tex]E(x) = \mu = x \cdot P(x) \\\\E(x) = \mu = 6 \cdot 0.64 + 8 \cdot 0.14 + 9 \cdot 0.14 + 15 \cdot 0.08 \\\\E(x) = \mu = 7.42[/tex]
The variance is given by
[tex]\sigma^2 = \sum (x - \mu)^2 \cdot p(x)[/tex]
[tex]\sigma^2 = (6 - 7.42)^2 \cdot 0.64 + (8 - 7.42)^2 \cdot 0.14 + (9 - 7.42)^2 \cdot 0.14 + (15 - 7.42)^2 \cdot 0.08 \\\\\sigma^2 = 1.291 + 0.0471 + 0.349 + 4.596 \\\\\sigma^2 = 6.283[/tex]
The standard deviation is given by
[tex]\sigma = \sqrt{\sum (x - \mu)^2 \cdot p(x)} \\\\\sigma = \sqrt{\sigma^2} \\\\\sigma = \sqrt{6.283} \\\\\sigma = 2.506[/tex]
Therefore,
Expected value or mean = [tex]E(x) = \mu = 7.42[/tex]
Variance = [tex]\sigma^2 = 6.283[/tex]
Standard deviation = [tex]\sigma = 2.506[/tex]
