A large piece factory equipment has a lifetime of 1 to 8 years with probabilities as indicated below:

Year 1 : Probability 0.04, Year 2 : Probability 0.06, Year 3 : Probability 0.08, Year 4 : Probability 0.18, Year 5 : Probability 0.24, Year 6 : Probability 0.24, Year 7 : Probability 0.12, Year 8 : Probability .04

1) Find the expected lifetime of this equipment, given that it lasts at least 6 years

2) Determine the probability that equipment that lasts more than 4 years, lasts more than 6 years

3) Determine the expected residual lifetime (future life) of equipment that is 4 years old and currently working

4) Determine the variance of the lifetime of the factory equipment

5) Determine that variance of the average lifetime of six pieces of factory equipment