064/21

Total Number of Questions : 27

Time : 2.00 Hours Max. Marks : 100

1. Apoint is chosen at random inside a circle. Find the probability that the point is more close to the
“centre of the circle than the circumference of the circle, (3 Marks)

2. Show that Binomial distribution belongs to the exponential family of distributions. (3 Marks)

-3. ॥ order to test whether a coin is perfect, it is tossed 5 times. The null hypothesis of perfectness is
tejected if and only if more than 4 heads are obtained. Find the probability of type | error. (3 Marks)

4. Give the layouts of a 4 x 4 Latin square design with the treatments A, 8, Cand 0. (3 Marks)
5. Define Binomial distribution. Find its mean and variance. (3 Marks)
x, O
6. Examine whether f(x) = 4 2—x, 1
0, otherwise is ap.d.f.
7, Define Hotelling's T?-statistics. (3 Marks)
8. What is the difference between random sampling and non-random sampling ? (3 Marks)
9. 5.1. sample variance is an unbiased estimate of the population variance. (3 Marks)
10. Explain the problem of auto-correlation in general regression model. (3 Marks)
“11. Define quadratic form. (3 Marks)
* 12. Define the following : (3 Marks)

i) Matrix

11 16617008801 matrix
iii) Rank of a matrix.

= 13. Define transition probability matrix. (3 Marks)

* 14. State Ergodic theorem. (3 Marks)

15. IfXisa random variable with mean a, show that the value of E(X-t} 15 minimum whent=a. (4 Marks)

ம்‌. ‏ہلا ہل اما‎ .... X, be a random sample from a population having uniform distribution in the interval

(0) ॥ + ४ ०) Find the estimators of ‏یر‎ and 6 ‏رط‎ the method of moments, (4 Marks)
17. Given ಗೃ: Median = 5. Compute T’, T-and 7 for the following observations :
6, 10, 3, 5, 2, 12 (4 Marks)
18. Define Weibull distribution. Find its mean and variance. (4 Marks)

0൬൩൧.