Discuss the below:
1. A manufacturer of electronics products expects that 1% of units fail during the warranty period. A sample of 600 independent units is tracked for warranty performance.
a) What is the expected number of failures during the warranty period?
b) What is the probability that none fails during the warranty period?
c) What is the probability that more than three units fail during the warranty period?
d) What is the probability that the number of failures will be between 1, 2, 3 standard deviations?
2. A binary message is transmitted as a signal S, which is either ? 1 or + 1. The communication channel corrupts the transmission with additive normal noise with = .1 and variance cr2 2.
The receiver concludes that the signal ? 1 was transmitted if the value received is < 0. What is the probability of error?
3. A system consists of two components connected a) in series ; b) in parallel. Suppose that i-th component has a lifetime that is exponentially distributed with ... = .01 and = .02, and that components fail independently. Let X = the time at which the system fails.
Calculate the cdf F(x) = P(X ≤ x), the pdf of X and the expected value of X for cases a) and b). Hint: use notation X = lifetime of i-th component, A = {X2
4.A stick of a length one is broken at random. Find the expected value of the difference between the larger part and the smaller part.