1) In the continuous distribution, probability density is provided by the function. Determine k, mean, variance and the distribution.
2)a) The number of monthly breakdowns of the computer is a random variable having the Poisson distribution with mean equal to 1.8. Determine the probability that this computer will function for the month
a) Without a breakdown
b) With at least one breakdown.
(b) If probability that the applicant for the driver’s license will pass the road test on any given trail is 0.8, find the probability that he will finally pass the test:
a) On the fourth trail and
b) less than four trails.
3) In the normal distribution, 7% of the items are under 35 and 89% of the items are under 63. Specify the mean and standard deviation of distribution.
4) Determine the correlation coefficient between X and Y using the following data.
X: 65 67 66 71 67 70 68 69
Y: 67 68 68 70 64 67 72 70
5) Fit the parabola by method of least squares to the following data also determine y at x=6.
X: 1 2 3 4 5
Y: 5 12 26 60 97
6) Customers reach at one man barber’s shop, as per the Poisson process with the mean inter arrival time of 12 min. Customers spend an average of 10 min in the barber’s chair.
a) What is the expected number of customers in barber shop and in queue?
b) Determine the percentage of customers who have to wait prior to get in to the barber’s chair?
c) Explain the probability that waiting time in the system is greater than 30 min?
18. There are 3 typists in an office. Every typist can type an average of the 6 letters per hour. If letters reach for being typed at rate of 15 letters per hour.
a) Find the fraction of time all the typists will be busy?
b) Explain the average number of letters waiting to be typed?
c) Determine the average time a letter has to spend for waiting and being for typed?