Mean and variance of six observations are 6 and 12 respectively. If each observation is multiplied by 3, then new variance of the resulting observations is
The variance of 20 observations is 5 . If each observation is multiplied by 3 and then 8 is added to each number, then variance of resulting observations is
If X is a random variable with distribution given below
| $\mathrm{X}=x_{\mathrm{i}}:$ | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| $\mathrm{P}\left(\mathrm{X}=x_{\mathrm{i}}\right):$ | $\mathrm{k}$ | $\mathrm{3k}$ | $\mathrm{3k}$ | $\mathrm{k}$ |
Then the value of $k$ and its variance are respectively given by
The mean and the standard deviation of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by $q$, where $p \neq 0$ and $q \neq 0$. If the new mean and new standard deviation (s.d.) become half of the original values, then $q$ is equal to
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