Question
Evaluate the following limits:
$\lim _{x \rightarrow 0}\left[\frac{(1-x)^8-1}{(1-x)^2-1}\right]$
$\lim _{x \rightarrow 0}\left[\frac{(1-x)^8-1}{(1-x)^2-1}\right]$
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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.
| No. of goals scored | 0 | 1 | 2 | 3 | 4 | 5 |
| No. of matches | 15 | 20 | 25 | 15 | 20 | 5 |
Compute the variance and standard deviation for the above data.