The DGC / 460 Assignm ent-3 Advanced/Statistical Methods: STAT 4303/5390 Total #

Question

The DGC / 460

Assignm ent-3 Advanced/Statistical Methods: STAT 4303/5390 Total # of pages: 14 ame Data generating code (DGC): It consists of first non-zero digit and the last two digits of your K- ID. Please write down your DGC here: DGC 46 Note: Keep accuracy up to at least four decimal places. Exercise 3.1. (KEEP PUBLIC PROPERTY NEAT AND CLEAN) An engineer designed an automatic railway crossing system by using three relays in parallel as shown below: B. Fig 3.1. Always watch railway crossing Instructor: Sarjinder Singh

Explanation / Answer

(a)

The system will function if atleast one of relay will function.

The probability of a relay malfunctions = DGC / (DGC + 500) = 460 / (460 + 500) = 0.4792

Probability that railway system malfunctions = Probability of all relay A, B and C malfunctions

= 0.4792 * 0.4792 * 0.4792 = 0.11

Probability that railway system will work = 1 - Probability that railway system malfunctions

= 1 - 0.11 = 0.89

b)

Let A be the event that Relay A functions and R be the event that railway system works.

Probability that the Relay A functions given the railway crossing system worked

= P(A | R) = P(R | A) P(A) / P(R) (By Bayes theorem)

Now,

P(A) = 0.4792, P(R) = 0.89

P(R | A) = 1 (As, all relays are in parallel, the probability of railway system working given relay A works is 1)

So,

Probability that the Relay A functions given the railway crossing system worked

= P(A | R) = P(R | A) P(A) / P(R) = 1 * 0.4792 / 0.89 = 0.5384

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