Each week, the number of acceptable? -quality units of a drug that are processed

Question

Each week, the number of acceptable? -quality units of a drug that are processed by a machine is observed: > l00, 50-l00, 1-50, 0 (indicating that the machine was broken (during the week). Given last week's observation, the probability distribution of next week's observation is as follows. > 100 50-100 1-50 0 >100 .8 .1 .05 .05 50-100 .1 .6 .1 .2 1-50 .1 .1 .5 .3 0 0 0 0 1 For example, if we observe a Week in which more than 100 units are produced, then there is a .10 chance that during the next week 50-100 units are produced. Suppose last week the machine produced 200 units. On average, how many weeks will elapse before the machine breaks down? Suppose last week the machine produced 50 units. On average, how many Weeks will elapse before the machine breaks down?

Explanation / Answer

a. Machine will brake down when 0 happens.

So, if last week the machine produced 200 units (that is >100) then probability that machine breaks down next week=0.05.

a. Machine will brake down when 0 happens.

So, if last week the machine produced 50 units (that is 50-100) then probability that machine breaks down next week=0.2.

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