Calculate Karl Pearson's coefficient of of correlation between x and y for the following data and interpret the result.
(1, 6), (2, 5), (3, 7), (4, 9), (5, 8), (6, 10), (7, 11), (8, 13), (9, 12)
r = = = There is a high positive correlation between the two variables.
x | y | xy | x2 | y2 |
1 | 6 | 6 | 1 | 36 |
2 | 5 | 10 | 4 | 25 |
3 | 7 | 21 | 9 | 49 |
4 | 9 | 36 | 16 | 81 |
5 | 8 | 40 | 25 | 64 |
6 | 10 | 60 | 36 | 100 |
7 | 11 | 77 | 49 | 121 |
8 | 13 | 104 | 64 | 169 |
9 | 12 | 108 | 81 | 144 |
45 | 81 | 462 | 285 | 789 |
The marks obtained by 10 candidates in English and Mathematics are given below.
Marks in English | 20 | 13 | 18 | 21 | 11 | 12 | 17 | 14 | 19 | 15 |
Marks in Mathematics | 17 | 12 | 23 | 25 | 14 | 8 | 19 | 21 | 22 | 19 |
Estimate the probable score for Mathematics if the marks obtained in English are 24.
A committee of 4 persons has to be chosen from 8 boys and 6 girls, consisting of at least one girl. Find the probability that the committee consists of more girls than boys.
An urn contains 10 white and 3 black balls while another urn contains 3 white and 5 black balls. Two balls are drawn from the second urn. Find the probability that the ball drawn from the second urn is a white ball.
Find the locus of a complex number, z = x + iy, satisfying the relation . Illustrate the locus of z in the Argand plane.
In an automobile factory, certain parts are to be fixed into the chassis in a section before it moves into another section. On a given day, one of the three persons A, B, C carries out this task. A has 45 % chance, B has 35 % and C has 20 % chance of doing the task. The probability that A, B and C will take more than the allotted time is respectively. I it is found that the time taken is more than the allotted time, what is the probability that A has done the mask?
The difference between mean and varianve of a bionomial distribution is 1 and the difference of their squares is 11. Find the distribution.