Mean and Variance of A Random Variable, Class 12 Mathematics NCERT Solutions

1. There will be total 10 MCQ in this test.
2. Please keep a pen and paper ready for rough work but keep your books away.
3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number.
4. No negative marking for incorrect choice.
5. Please click on “Finish the Test” when you want to exit.
6. All the best – Happy Studying.

1. In a series of 2 n observations, half of them equal ‘a’ and remaining half equal – a. If the standard deviation of the observations is 2, then | a | equals ……

 √2/n

 2

 1/n

 √2

Question 1 of 10

2. Let X be a random variable whose possible values x₁, x₂, x₃, …, x_n occur with probabilities p₁, p₂, p₃,…, p_n, respectively. The mean of X, denoted by

 A

 B

 C

 D

Question 2 of 10

3. The number of adults living in homes on a randomly selected city block is described by the following probability distribution.
What is the probability that 4 or more adults reside at a randomly selected home?

  .50

 .25

 .10

 .15

Question 3 of 10

4. Two dice are thrown simultaneously. If X denotes the number of sixes, then the expectation of X is:

 1/3

 1/2

 1/4

  1/6

Question 4 of 10

5. Let X be a random variable whose possible values x₁, x₂, x₃, …, x_n occur with probabilities p₁, p₂, p₃,…, p_n, respectively. Also, μ be the mean of X. The variance of X, denoted by Var (X) is defined as

A. B. C. D.

 A

 B

 C

 D

Question 5 of 10

6. The variance of the number obtained on a throw of an unbiased dice is:

 0

 35/12

 91/36

 1

Question 6 of 10

7. The mean number of tails in three tosses of a fair coin is:

  3/2

 1/6

 6

 3

Question 7 of 10

8. A class has 10 students whose ages are 15, 14, 16, 17, 19, 20, 16, 18, 20, and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. The standard deviation of X is:

  17.5

 4.45

 2.11

 4.41

Question 8 of 10

9. Let X be a random variable whose possible values x₁, x₂, x₃, …, x_n occur with probabilities p₁, p₂, p₃,…, p_n, respectively. Also, E(X) is the expectation of X, then is known as

 Variance

 Standard deviation

 Mean x variance

 Mean

Question 9 of 10

10. In a meeting, 60% of the members favour and 40% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X).

  0.6 and 0

 0.6 and 0.44

  0.6 and 0.24

 0.4 and 0.24

Question 10 of 10

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