Could anyone point me in the right direction in terms of how to approach the following questions based on the scenario below. If you could just break down what needs to be done in simple English, that would be really helpful…. In particular, I need guidance on how to go about making a table for the probability distribution in relation to this example – I am finding all the heads and tails confusing. Also is there a formula which should be used to find the mean of this type of distribution? Thanks in advance.


Scenario

Suppose you bought some really cheap blank DVDs at the dollar store. Then you look them up on the web and find that half these disks are dead on arrival and when data are recorded on the remainder, about half of those become unreadable within the first year, half of the survivors die in the second year, etc. Let's see what happens over seven years. We can model the distribution of "time before failure" with a coin toss.


Questions:


  1. Make a table for the probability distribution of the number of tosses before you got a head (=failure). For example this random variable assigns 3 to TTTHTHT and 0 to HTHTHTH, meaning one disk lasted three years and another was dead on arrival. (Make sure you get the right counts for these two examples before you continue.) If you never get a head (TTTTTTT), assign the value 7.
  2. What do your probabilities add up to?
  3. Often of interest in such situations is the mean time before failure (MTBF). This is a common spec for computer hard drives. Find this for the distribution above.