Question
Find $\left(50^2-49^2\right)+\left(48^2-47^2\right)+\left(46^2-45^2\right)+\ldots \ldots+\left(2^2-1^2\right)$
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| X | 1 | 3 | 5 | 7 | 9 |
| Frequency | 5 | 10 | 20 | 10 | 5 |
Age | 16 | 17 | 22 | 19 | 21 | 16 |
Marks | 16 | 19 | 39 | 50 | 48 | 41 |
Age | 21 | 20 | 20 | 23 | 22 | 19 |
Marks | 59 | 44 | 42 | 62 | 37 | 67 |
Age | 23 | 20 | 22 | 22 | 23 | 22 |
Marks | 45 | 57 | 35 | 37 | 38 | 56 |
Age | 17 | 18 | 16 | 21 | 19 | 20 |
Marks | 54 | 61 | 47 | 67 | 49 | 56 |
Age | 17 | 18 | 23 | 21 | 20 | 16 |
Marks | 51 | 42 | 65 | 56 | 52 | 48 |
Prepare a bivariate frequency distribution by taking class intervals 16 – 18, 18 – 20,…,etc. for age and 10 – 20, 20 – 30,…, etc. for marks.
Find
(i) marginal frequency distributions.
(ii) conditional frequency distribution of marks obtained when age of students is between 20 – 22.
Price | 5 | 7 | 9 | 8 | 10 | 7 | 9 | 8 | 5 | 11 | 11 | 10 | 2 | 3 | 9 |
| Demand | 9 | 15 | 13 | 15 | 14 | 10 | 11 | 14 | 10 | 14 | 6 | 14 | 15 | 11 | 12 |
Price | 2 | 4 | 3 | 14 | 6 | 10 | 7 | 15 | 8 | 6 | 5 | 6 | 11 | 14 | 15 |
| Demand | 6 | 11 | 8 | 11 | 10 | 15 | 9 | 15 | 13 | 9 | 14 | 10 | 7 | 5 | 6 |
Classify the data by taking classes 0 – 4, 5 – 9, etc. for X and 5 – 8, 9 – 12, etc. for Y.
Also find
(i) marginal frequency distribution of X and Y.
(ii) conditional frequency distribution of Y when X is less than 10.
$\lim _{v \rightarrow \sqrt{2}}\left[\frac{v^2+v \sqrt{2}-4}{v^2-3 v \sqrt{2}+4}\right]$