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Mathematics

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valina [46]3 years ago

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I think 28fa haha s an

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

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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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