Let the mean and the standard deviation of the probability distribution
| $$\mathrm{X}$$ | $$\alpha$$ | 1 | 0 | $$-$$3 |
|---|---|---|---|---|
| $$\mathrm{P(X)}$$ | $$\frac{1}{3}$$ | $$\mathrm{K}$$ | $$\frac{1}{6}$$ | $$\frac{1}{4}$$ |
be $$\mu$$ and $$\sigma$$, respectively. If $$\sigma-\mu=2$$, then $$\sigma+\mu$$ is equal to ________.
The variance $$\sigma^2$$ of the data
| $$x_i$$ | 0 | 1 | 5 | 6 | 10 | 12 | 17 |
|---|---|---|---|---|---|---|---|
| $$f_i$$ | 3 | 2 | 3 | 2 | 6 | 3 | 3 |
is _________.
If the mean and variance of the data $$65,68,58,44,48,45,60, \alpha, \beta, 60$$ where $$\alpha> \beta$$, are 56 and 66.2 respectively, then $$\alpha^2+\beta^2$$ is equal to _________.
The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12 . If $$\mu$$ and $$\sigma^2$$ denote the mean and variance of the correct observations respectively, then $$15\left(\mu+\mu^2+\sigma^2\right)$$ is equal to __________.
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