how does multiplying powers with the same base differ from multiplying powers with the same exponent but different bases?
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Answer:
Expected load loss = 1.35
P (Load Loss) = 0.127
Step-by-step explanation:
The probability of failure is: <em>q</em> = 0.015
The probability of success is: <em>p</em> = 1 - <em>q</em> = 1 - 0.015 = 0.985
The number of units the generation system is composed of is, <em>n</em> = 9.
The capacity of each unit is 10 MW.
Let <em>X</em> = number of units that failed or are unavailable.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>q.</em>
The probability function is:
; <em>x</em> =0, 1, 2, 3...
- The expected number of failures is:
Then the expected load loss is:
Thus, the expected load loss is 1.35.
- The load loss will be when at least one unit fails.
The probability that at least one unit fails is:
P (X ≥ 1) = 1 - P (X < 1) = 1 - P (X = 0)
Thus, the probability of load loss is 0.127.