If the mean and variance of a binomial variate X are $\frac{4}{3}, \frac{8}{9}$respectively, then P(X = 2) =

• $\frac{4}{27}$

• $\frac{16}{81}$

• $\frac{8}{27}$

• $\frac{8}{81}$

The variance of the following data is

xi	6	10	14	1	24	28	30
fi	2	4	7	12	8	4	3

• 33.4

• 34.3

• 43.4

• 44.3

$$\begin{gathered} \mathrm{If} \mathrm{\alpha } \ne 0, \mathrm{and} \mathrm{the} \mathrm{mean} \mathrm{deviation} \mathrm{of} \mathrm{the} \mathrm{observations} \\ \left\{\mathrm{k\alpha }\right\}, \mathrm{for} \mathrm{k} = 1, 2, ..., 50 \mathrm{about} \mathrm{its} \mathrm{median} \mathrm{is} 50, \mathrm{then} \left|\mathrm{\alpha }\right| = ? \end{gathered}$$

• 4

• 3

• 2

• 5

Let X = $\left\{\mathrm{x} \in \mathrm{N} : 1 \le 1 \le 17\right\}$ and Y = {ax + b : x $\in$ X and a, b $\in$ R, a > 0}. If mean and variance of elements of Y are 17 and 216 respectively then a + b is equal to :

• 7

• 9

•  - 7

•  - 27

Let the data 4, 10, x, y, 27 be in increasing order. If the median of data is 18 and its mean deviation about mean is 7.6 then the mean of this data is :

• 17

• 16

• 16.5

• 15.5

$$\begin{gathered} \mathrm{Let} {\mathrm{x}}_{\mathrm{i}}\left(1 \le \mathrm{i} \le 10\right) \mathrm{be} \mathrm{ten} \mathrm{observation} \mathrm{of} \mathrm{a} \mathrm{random} \mathrm{variable} \mathrm{X}. \mathrm{If} \sum _{\mathrm{i} = 1}^{10}\left({\mathrm{x}}_{\mathrm{i}} - \mathrm{p}\right) = 3 \\ \mathrm{and} \sum _{\mathrm{i} = 1}^{10}{\left({\mathrm{x}}_{\mathrm{i}} - \mathrm{p}\right)}^2 = 9 \mathrm{where} 0 \ne \mathrm{p} \in \mathrm{R}, \mathrm{then} \mathrm{the} \mathrm{standard} \mathrm{deviation} \mathrm{of} \mathrm{these} \mathrm{observations} \mathrm{is} \end{gathered}$$

• $\frac{4}{5}$

• $\sqrt{\frac{3}{5}}$

• $\frac{9}{10}$

• $\frac{7}{10}$

The mean and variance of 8 observations are 10 and 13.5 respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is :

• 9

• 5

• 3

• 7

If the variance of the following frequency distribution :

Class :      10-20 20-30 30-40

Frequency : 2        x        2

is 50, then x is equal to ....

The mean and variance of 7 observations are 8 and 16, respectively. If five observation are 2, 4, 10, 12, 14 then the absolute difference of the remaining two observations is :

• 1

• 2

• 3

• 4

50.

If the mean and the standard deviation of the data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation : 

• x² - 20x + 18 = 0

• 2x² - 20x + 19 = 0

• x² - 10x + 19 = 0

• x² - 10x + 18 = 0