A system contains 4 components, at least 3 of which must function in order for t
ID: 3181649 • Letter: A
Question
A system contains 4 components, at least 3 of which must function in order for the system to function. At a given time, the number of components, n, that are not functioning has the probability distribution given below.
(a) What is the mean number of components functioning at any time? (b) What is the standard deviation of the number of components functioning at any time? (c) What is the probability that the system functions? Does this contradict the answer to part (a)?
n 0 1 2 3 4 Prob 0.55 0.05 0.02 0.15 0.23Explanation / Answer
Mean = 0* 0.55 +1 *0.05+ 2*0.02+3*0.15+4*.23 = 1.46
Variance= 0.55* (1.46-0)^2 + 0.05*(1.46-1)^2 + 0.02 * (1.46-2)^2 + 0.15 * (3-1.46)^2 + 0.23 * (4-1.46)^2 =3.0284
Standard Deviation = sqrt(3.0284) = 1.74023
Probability system functions = P(0 failure) + P( 1 failure) = 0.55+0.05 = 0.60
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.