The distribution function of Pareto distribution is given by ,
.
Given a , generate a random number from the above distribution, when
and
.
Suppose , then find x.
The cumulative distribution function (CDF) of the Pareto distribution is given as: [ F(x) = 1 - \left(\frac{k}{x}\right)^a ] Here, (a = 2), ______ ____ ___ _______ ________ _____ ________ ________.
___ ____ _________ ________ _________.
___ _______ ________ ______ _______ ___ ___ ________ __________ _________.
_______ __________ _________ ____ _____ _________.
_________ _______ _________ ________ ______.
____ ______ _________ ________ __________ ____ ________ ______ ______ _____.
_________ _______ _____ _______ _________ ________ _____ ___ ________ _____.
_____ _________ __________ _____ _______ _________ _______.
__________ ____ ____ ____ ______ _______ ____ ____ __________.
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The following data relate to production in kg of three varieties P, Q, R of wheat:
| P : | 14 | 16 | 18 | ||
| Q: | 14 | 13 | 15 | 22 | |
| R : | 18 | 16 | 19 | 15 | 20 |
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.
A researcher wants to test four diets A, B, C, D on growth rate in mice. These animals are divided into 3 groups according to their weights. Heaviest 4, next 4 and lightest 4 are put in Block I, Block II, and Block III, respectively. Within each block, one of the diets is given at random to the animals. After 15 days, increase in weight is noted, which is given in the following table:
| Blocks | Treatments/Diets | |||
|---|---|---|---|---|
| A | B | C | D | |
| I | 12 | 8 | 6 | 5 |
| II | 15 | 12 | 9 | 6 |
| III | 14 | 10 | 8 | 5 |
The distribution function of Pareto distribution is given by ,
.
Given a , generate a random number from the above distribution, when
and
.
Suppose , then find x.
Generate a complete cycle for the LCG given below: , with
. A man tosses an unbiased coin ten times. Using the first ten random numbers generated above, obtain a sequence of heads and tails by taking Head (H) as
.
Identify the design given in the following table and then carry out the analysis:
| Column | Row | |||
|---|---|---|---|---|
| I | II | III | IV | |
| I | A 8 | C 18 | B 11 | D 8 |
| II | C 16 | B 10 | D 7 | A 4 |
| III | B 12 | D 10 | A 6 | C 20 |
| IV | D 10 | A 9 | C 28 | B 16 |
Draw all possible samples of size 2 from the population [2, 3, 4] and verify that . Also find variance of
.