If X is a random variable with E(X) = 3and E(X2) = 16, find a lower bound for the probability P[-2 < X < 8].
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In a certain community, 10% of all people above 50 years of age have diabetes. A health service in this community correctly diagnoses 95% of all persons with diabetes as having the disease, and incorrectly diagnoses 5% of all persons without diabetes as having the disease. Find the probability that a person randomly selected from among all people of age above 50 and diagnosed by the health service as having
diabetes actually has the disease.
Let X and Y have the continuous joint distribution with p.d.f.
where a > 0.Compute the marginal densities of X and Y. Check whether X and Y are independent.
Let the p.d.f. of a continuous random variable X be given by
Find the maximum likelihood estimator of based on a sample X1 ,X2 ,....,Xn .
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.
Let X1 ,X2 ,...,Xn be a random sample from a normal population, N(.Obtain a (1-
) level confidence interval for
when
is unknown.
If X is a random variable with E(X) = 3and E(X2) = 16, find a lower bound for the probability P[-2 < X < 8].
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 |