Please help with either problem. Applications of Markov Chains, Independence, Ba
ID: 3062502 • Letter: P
Question
Please help with either problem. Applications of Markov Chains, Independence, Bayes Rule.
6. (extra 10 points) Applications of Markov chains: Describe an engineering problem of your choice in which you can apply any type of Markov chain. You need to provide an example at the level of detail similar to the channel-access examples we discussed in class. By now you notice that with the proper simplifying assumptions you can make a Markov chain out of many engineering problems. 7. (extra 10 points) Applications of Independence or Bayes Rule: Describe an engineering problem of your choice in which independence or Bayes rule is used. Your example must be at the level of detail similar to what we covered in class (the analysis of logic circuits or the robot opening the door)Explanation / Answer
Answer- 7.
Example related to engineering-
Machines A and B produce 10% and 90% respectively of the production of a component intended for the motor industry. From experience, it is known that the probability that machine A produces a defective component is 0.01 while the probability that machine B produces a defective component is 0.05.
With the above given information we can calculate the following probabilities -
If a component is selected at random from a day’s production and is found to be defective, find the probability that it was made by
(a) machine A;
. Let us denote the folloiwng events-
A = {item from machine A}, B = {item from machine B}, D = {item is defective}.
We know that: P(A)=0.1, P(B)=0.9, P(D|A)=0.01, P(D|B)=0.05.
P(A|D) = P(D|A)P(A) / [ P(D|A)P(A) + P(D|B)P(B) ]
= 0.01 × 0.1 0.01 × 0.1+0.05 × 0.9
= 0.02
(b) machine B.
Similarly P(B|D)=0.98
Thanks!