1
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The p.m.f. of a random variable $$\mathrm{X}$$ is $$\mathrm{P}(x)=\left\{\begin{array}{cl}\frac{2 x}{\mathrm{n}(\mathrm{n}+1)}, & x=1,2,3, \ldots \mathrm{n} \\ 0, & \text { otherwise }\end{array}\right.$$, then $$\mathrm{E}(\mathrm{X})$$ is

A
$$\frac{\mathrm{n}+1}{6}$$
B
$$\frac{2 \mathrm{n}+1}{6}$$
C
$$\frac{\mathrm{n}+1}{3}$$
D
$$\frac{2 n+1}{3}$$
2
MHT CET 2023 14th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The variance of 20 observations is 5. If each observation is multiplied by 2, then variance of resulting observations is

A
5
B
10
C
4
D
20
3
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Variance of first $$2 n$$ natural numbers is

A
$$\frac{4 n^2+1}{12}$$
B
$$\frac{(2 n-1)^2}{12}$$
C
$$\frac{n^2}{3}-1$$
D
$$\frac{4 n^2-1}{12}$$
4
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the sum of the mean and the variance of a binomial distribution for 5 trials is 1.8 , then the value of $$p$$ is

A
0.4
B
0.8
C
0.18
D
0.2
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