Table of Contents
Chapter 32 Mean and variance of a random variable Exercise Ex. 32.1
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 18
Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
Solution 21
Question 22
Solution 22
Question 23
Solution 23
Question 24
Solution 24
Question 25
Solution 25
Question 26
Solution 26
Question 27
Solution 27
Question 28
Four balls are to be drawn without replacement from a box containing 8 red and 4 white balls. If X denotes the number of red balls drawn, find the probability distribution of X.Solution 28
Question 29
The probability distribution of a random variable X is given below:
(i) Determine the value of k
(ii) Determine P (X 2) and P b(X > 2)
(iii) Find P (X 2) + P(X > 2)Solution 29
Chapter 32 Mean and variance of a random variable Exercise Ex. 32.2
Question 1(i)
Find the mean and standard deviation of each of the following probability distributions:
xi : 2 3 4
pi : 2.2 0.5 0.3Solution 1(i)
Question 1(ii)
Solution 1(ii)
Question 1(iii)
Solution 1(iii)
Question 1(iv)
Solution 1(iv)
Question 1(v)
Solution 1(v)
Question 1(vi)
Solution 1(vi)
Question 1(vii)
Solution 1(vii)
Question 1(viii)
Solution 1(viii)
Question 1(ix)
Find the mean and standard deviation of each of the following probability distributions:
Solution 1(ix)
Question 2
A discrete random variable X has the probability distribution given below:
X : 0.5 1 1.5 2
P(X) : k k2 2k2 k
(i) Find the value of k.
(ii) Determine the mean of the distribution.Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Three cards are drawn at random (without replacement) from a well shuffled pack of 52 cards. Find the probability distribution of number of red cards. Hence find the mean of the distribution.Solution 17
Question 18
An urn contains 5 are 2 black balls. Two balls are randomly drawn, without replacement. Let X represent the number of black balls drawn. What are the possible values of X? Is X a random variable? If yes, find the mean and variance of X.Solution 18
Question 19
Two numbers are selected at random (without replacement) from positive integers 2,3,4,5, 6 and 7. Let X denote the larger of the two number obtained. Find the mean and variance of the probability distribution of X.Solution 19
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