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.
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Let X be a r.v. with p.m.f. given by the following table:
| - 2 | - 1 | 0 | 1 | 2 |
| 3 20 | 4 20 | 6 20 | 4 20 | 3 20 |
Obtain the maximum likelihood estimate of in
based on an independent sample of size n.
Prove that
for all m > 0, n > 0.Hence evaluate (10,7) and
.
For a Poisson distributed random variable X, P(X = 4) = P(X = 5).What is the mean and variance of the distribution?
The height of 100 students of a study centre of IGNOU is approximately normally distributed with mean () 65 inches and standard deviation (
) 2.5 inches. Find the number of students whose height is
i) less than 65 inches,
ii) between 60 inches and 70 inches.
For the following data
| x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| f | 1 | 9 | 26 | 59 | 72 | 52 | 29 | 7 | 1 |
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 .