1) Write down the properties of Binomial distribution.
2) A die is thrown 6 times. Evaluate individual and cumulative probabilities of different possible events if getting of Two is treated is success in each trail. Therefore determine the probability of getting two at least once and probability of two not getting.
3) Derive relationship between f(t), F(t), h(t), R(t).
4) Consider a system consisting of 6 identical units of each having a failure rate of 0.2 failures per year.
i. Estimate the probability of success of the system if it is fully redundant configuration for a period of 1000 hours.
ii. Estimate the probability of system surviving at least 4 out of 6 units should be success for a period of 1000 hours. Suppose the exponential distribution with constant hazard rate function for the probability of components.
5) Write detailed notes on Bath Tub curve.
6) Consider a system comprising of 4 identical units with having failure rate of 0.1 f/yr. Estimate the probability of the system surviving ‘5’ years, if at least 2 units should operate successfully.