An insurance company models the number of days elapsing between the beginning of a calendar year and the moment a high-risk driver gets into an accident by means of an exponential random variable with parameter . If they expect that 10% of the high-risk drivers will get into an accident during the first 30 days of the calendar year, find the probability that a high-risk driver will get into an accident during the first 40 days of a calendar year.
i) What is the probability that the mean length of service times is more than and equal to 12 minutes.
ii) Find the 99% confidence interval for the standard deviation of the mean length of service times.
A newspaper publisher, trying to pinpoint his market’s characteristics wondered whether newspaper readership in the community is related to readers’ educational achievement. A survey questioned adults in the area on their level of education and their frequency of readership. The results are shown in the following table:
| Frequency of Readership | Level of Educational Achievement | |||
| Professional or postgraduates | College graduates | High school grad | Did not complete high school | |
| Never | 10 | 17 | 11 | 21 |
| Sometimes | 12 | 23 | 8 | 5 |
| Morning or evening | 35 | 38 | 16 | 7 |
| Both editions | 28 | 19 | 6 | 13 |
A system has eight independent components and reliability block diagram of it shown blow.
Components 1, 2 and 3 are not identical and at least two component of this group must be available for system success. The reliability of component 1 to 8 (for a mission 1 year) is given below
R6 = R7 = R8 = 0.80 ,R1 = 0.60 , R2 = 0.40, R3 = 0.50 and R4 = 0.60. Find reliability of the system.
An urn contains 10 white marbles, 15 blue marbles, and 20 red marbles. Five marbles are selected, one at a time, with replacement. Find the probability that at least one color will be missing from the 10 selected marbles
For a factorial experiment with 3 factors, N, P and M each at two levels, the design and yield per plot are given below. Analyse the experiment.
Replicate – I
| Block - 1 | np 48.81 | nm 58.88 | pm 46.11 | (1) 38.62 |
| Block - 2 | m 40.49 | p 32.75 | npm 61.55 | n 55.07 |
| Block -3 | np 50.43 | pm 52.31 | (1) 40.26 | np 49.62 |
| Block -4 | m 32.36 | p 51.94 | npm 48.89 | n 53.86 |
| Block -5 | n 47.3.7 | npm 46.87 | p 37.25 | m 46.94 |
| block -6 | pm 39.30 | (1) 39.23 | nm 49.93 | np 51.43 |
If the probability density function of a random variable X follows F-distribution is
then degrees of freedom of the distribution will be (2,2).
What is the average length of the queen that forms from time to time?