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mel-nik [20]
3 years ago
9

Data collected over time on the utilization of a computer core (as a proportion of the total capacity) were found to possess a r

elative frequency distribution that could be approximated by a beta density function with α = 2 and β = 4. Find the probability that the proportion of the core being used at any particular time will be less than 0.10.
Mathematics
1 answer:
Marianna [84]3 years ago
3 0

Answer:

The probability that the proportion of the core being used at any particular time will be less than 0.10 is 0.08146

Step-by-step explanation:

\mu =\frac{\alpha }{\alpha +\beta  } = \frac{1}{1 + \frac{\beta}{\alpha} } 1/3   0.33  = 33.33 %

       The Probability of that the proportion of the core being used at any particular time will be less than 0.10 is given by  

PDF = \frac{x^{\alpha -1} (1-x)^{\beta -1} }{\int\limits^1_0 {u^{\alpha -1} (1-u)^{\beta -1}} \, du }

where x = 0.1

α = 2 and β = 4

PDF = \frac{0.0729 }{\int\limits^1_0 {u^{\alpha -1} (1-u)^{\beta -1}} \, du } = 1.458  

CDF = \frac{\int\limits^{0.1}_0 {t^{\alpha -1} (1-t)^{\beta -1}} \, du }{\int\limits^1_0 {u^{\alpha -1} (1-u)^{\beta -1}} \, du } = 0.08146

The probability that the proportion of the core being used at any particular time will be less than 0.10 = 0.08146.

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