Respuesta :
Answer:
Expected load loss = 1.35
P (Load Loss) = 0.127
Step-by-step explanation:
The probability of failure is: q = 0.015
The probability of success is: p = 1 - q = 1 - 0.015 = 0.985
The number of units the generation system is composed of is, n = 9.
The capacity of each unit is 10 MW.
Let X = number of units that failed or are unavailable.
The random variable X follows a Binomial distribution with parameters n and q.
The probability function is:
[tex]P (X=x)={n\choose x}p^{x}(1-p)^{n-x}[/tex]; x =0, 1, 2, 3...
- The expected number of failures is:
[tex]E(X)=nq=9\times0.015=0.135[/tex]
Then the expected load loss is:
[tex]E (Load\ Loss)=10\times E(X)=10\times 0.135=1.35[/tex]
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)
[tex]=1-[{9\choose 0}(0.015)^{0}(1-0.015)^{9-0}]\\=1-0.8728\\=0.12718\\\approx0.127[/tex]
Thus, the probability of load loss is 0.127.
