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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In the following data, two values are missing. Estimate these values by Yates method and analyse the data by suitable technique.
| Treatments | Blocks | ||
|---|---|---|---|
| I | II | III | |
| A | 12 | 14 | 12 |
| B | 10 | y | 8 |
| C | x | 15 | 10 |
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.
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 |
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:
| Plot No. | Group 1 | Group 2 | Group 3 | Group 4 | Group 5 | Group 6 |
|---|---|---|---|---|---|---|
| 1 | 8 | 6 | 18 | 13 | 17 | 12 |
| 2 | 13 | 5 | 8 | 7 | 15 | 15 |
| 3 | 11 | 16 | 6 | 13 | 10 | 11 |
| 4 | 26 | 5 | 10 | 6 | 21 | 17 |
| 5 | 13 | 16 | 16 | 7 | 20 | 8 |
| 6 | 31 | 5 | 20 | 2 | 25 | 10 |
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 |
Draw all possible samples of size 2 from the population [2, 3, 4] and verify that . Also find variance of
.
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:
| Villages | Stratum sizes ($N_i$) | Means ($x_i$) | Standard deviations |
|---|---|---|---|
| Village A | 400 | 60 | 20 |
| Village B | 200 | 120 | 80 |