Question6 (a) The process s(t) is wide sense stationary (wss) with R,(t) e-2[TUT

Question

Question6 (a) The process s(t) is wide sense stationary (wss) with R,(t) e-2[TUT. We want to find an estimate of s(t - T/3) in terms of s(t) and s(t -T/2) as follows: E(S(t-T/3) |s(t), s(t-T/2)) = as(t) + bs(t-T/2) (i) Determine the constants and b. [8 marks] (ii) Find the mean square error. [5 marks] (b) We have four boxes. Boxes 1 and 2 contain 500 components of which 5% are defective. Box 3 contains 1000 components of which 20% are defective, and Box 4 contains 200 components of which 10% are defective. We select at random one of the boxes and we remove at random two single components. (i) Calculate the probability that both selected components are defective. [9 marks] (ii) Calculate the probability that the selected components came from Box 3, given that both were found to be defective. [3 marks]

Explanation / Answer

b)

a) P(selected component is defective )=P( box 1 and defective+box 2 and defective+box 3 and defective+box 4 and defective) =(1/4)*0.05+(1/4)*0.05+(1/4)*0.2+(1/4)*0.1=0.1000

b) probability ( it came from box 3 ; given defective) =P(box 3 and defective)/P( defective)

=(1/4)*0.2/0.1000=0.5

Hope this will be helpful. thanks and god Bless you :-)

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