State whether the following statements are true or false and also give the reason in support of your answer:
(a) The total number of all possible samples of size 2 without replacement from a population of size 7 is 21.
(b) Consecutive 3 random numbers starting from 8937 by 'middle square method' are 8937, 8699, 6726.
(c) RBD is suitable in situations where it is not possible to divide the experimental material into a number of homogeneous blocks.
(d) As we increase the sample size, representativeness of the population by the sample decreases.
(e) In a big hall, there are 50 rows and each row has 60 students. A research scholar selects 10 rows randomly and then randomly selects 15 students from each selected row. It is an example of cluster sampling procedure

The following data relate to production in kg of three varieties P, Q, R of wheat:

Times between successive crashes of a computer system were generated for a 6-month period and are given in increasing order as follows (time in hours):

The distribution function of Pareto distribution is given by f(x) = 1 - (k/x)^a   , a >0 , 0 < k ≤ x.
Given a U~ U(0, 1), generate a random number from the above distribution, when a = 2 and k = 1. Suppose U = 0.5, then find x

Draw all possible samples of size 2 from the population [2, 3, 4] and verify that E ( x̄ ) = x̄  . find variance of x̄

A sample of 60 students is to be drawn from a population consisting of 600 students belonging to two villages, A and B. The means and standard deviations of their marks are give below:

To determine the yield rate of wheat in a district of Punjab, 6 groups of 6 plots each were constructed. The data are given in the following table: