1
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The discrete random variable $$\mathrm{X}$$ can take all possible integer values from 1 to $$\mathrm{k}$$, each with a probability $$\frac{1}{\mathrm{k}}$$, then its variance is

A
$$\frac{\mathrm{k}^2-1}{12}$$
B
$$\frac{\mathrm{k}^2-1}{6}$$
C
$$\frac{\mathrm{k}^2+1}{12}$$
D
$$\frac{\mathrm{k}^2+1}{6}$$
2
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

For 20 observations of variable $x$, if $$\sum\left(x_i-2\right)=20$$ and $$\sum\left(x_i-2\right)^2=100$$, then the standard deviation of variable $$x$$ is

A
2
B
3
C
4
D
9
3
MHT CET 2023 12th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the variance of the numbers $$-1,0,1, \mathrm{k}$$ is 5, where $$\mathrm{k} > 0$$, then $$\mathrm{k}$$ is equal to

A
$$2 \sqrt{\frac{10}{3}}$$
B
$$2 \sqrt{6}$$
C
$$4 \sqrt{\frac{5}{3}}$$
D
$$\sqrt{6}$$
4
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If both mean and variance of 50 observations $$x_1, x_2, \ldots \ldots, x_{50}$$ are equal to 16 and 256 respectively, then mean of $$\left(x_1-5\right)^2,\left(x_2-5\right)^2, \ldots \ldots\left(x_{50}-5\right)^2$$ is

A
357
B
387
C
377
D
397
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