a) number (N) is safety incidents per month which correlates with following table: n 0-2 3 4 5 ≥6 Pr(N = n) 0.15 0.27 k 0.12 0.15 i) find the value of k ii) over last 12 months, there was two months where there was atleast 6 safety incidents per month. use binomial distribution to estimate probability of this occuring.
a)
number (N) is safety incidents per month which
| n | 0-2 | 3 | 4 | 5 | ≥6 |
| Pr(N = n) | 0.15 | 0.27 | k | 0.12 |
0.15 |
i) find the value of k
ii) over last 12 months, there was two months where there was atleast 6 safety incidents per month. use binomial distribution to estimate
b)
car make and model is under warranty for the first 10 years after purchased, so major repairs after this time will have to be payed by the customer. The number of years, T after been purchased until customer must pay for major repairs is distributed by the *attached* probability density
i) What is the probability that customer will have to pay for major repairs less then 18 years after initial purchase?
ii) From the attached equation, it is shown that expected time until customer would have to pay for major repairs is E(T) ≈ 13.86. With this information determine the variance, Var(T) of varaible T.
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for part ii) why was for the
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