For the following frequency table obtain the relative frequencies and the cumulative frequencies of the ‘more than’ type.
| Life (in hours)
499.5 – 649.5 | Frequency
5 |
| 649.5 – 799.5 | 20 |
| 799.5 – 949.5 | 40 |
| 949.5 – 1099.5 | 81 |
| 1099.5 – 1249.5 | 57 |
| 1249.5 – 1399.5 | 34 |
| 1399.5 – 1549.5 | 13 |
| Total | 250 |
Also determine the number of bulbs having a life of 1249.5 hours or less.
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There are three urns, urn 1 having 5 white and 3 black balls, urn II with 4 white and 4 black balls and urn III with 3 white and 5 black balls. A fair die is tossed and
i) urn I is chosen if dice shows up 1, 2 or 3,
ii) urn II is chosen if dice shows up 4 or 5,
iii) urn III is chosen if dice shows up 6.
2 balls are drawn at random from the chosen urn. What is the probability that one of the balls drawn is white and the other black?
6 observations on (X,Y) yielded the following data:
i) Determine the correlation coefficient between X and Y.
ii) Given X =10 , what will be the predicated value of Y?
iii) Given Y = 15, predict X.
X is a random variable taking values 0 and 1 with respective probabilities q and p. A sample X1 , X2 ,...., Xn of size n is taken from the distribution.If , shows that the bias of the estimator tends to zero as n tends to infinity.
For the following data
| x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| f | 1 | 9 | 26 | 59 | 72 | 52 | 29 | 7 | 1 |
If a random variable U has the t-distribution with n degrees of freedom, show that Z = U2 has the F-distribution with 1 and n degrees of freedom.
A random sample of 16 observations from a normal distribution yields the values
Find a 95% confidence interval for the variance of the normal distribution.
Suppose X has the density function
Find its moment generating function whenever it exists.