Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Business Maths Guide Pdf Chapter 6 Random Variable and Mathematical Expectation Ex 6.3 Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 6 Random Variable and Mathematical Expectation Ex 6.3

Question 1.
Value which is obtained by multiplying possible values of random variable with probability of occurrence and is equal to weighted average is called
(a) Discrete value
(b) Weighted value
(c) Expected value
(d) Cumulative value
Solution:
(c) Expected value

Question 2.
Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0.29, 0.40, 0.35. Profit per unit is 0.50 paisa then expected profits for three days are
(a) 21, 19, 22
(b) 21.5, 19.5, 22.5
(c) 0.29, 0.40, 0.35
(d) 3.045, 3.8, 3.85
Solution:
(d) 3.045, 3.8, 3,85
Hint:

 x 21 19 22 P(x) 0.29 0.4 0.35

E(X) = $$\sum_{ x }$$ xP(x)
For Day 1
E(X) = 21 × 0.29
= 6.09
Expected profit = 6.09 × 0,50 = 3.054
For Day 2
E(X) = 19 × 0.40
= 7.6
Expected Profit = 7.6 × 0.50 = 3.8
For Day 3
E(X) = 22 × 0.35
= 7.7
Expected Profit = 7.7 × 0.50 = 3.85

Question 3.
Probability which explains x is equal to or less than particular value is classified as
(a) discrete probability
(b) cumulative probability
(c) marginal probability
(d) continuous probability
Solution:
(b) Cumulative Probability

Question 4.
Given E(X) = 5 and E(Y) = -2, then E(X – Y) is
(a) 3
(b) 5
(c) 7
(d) -2
Solution:
(c) 7
Hint:
E(x – 7) = E(x) – E(y) = 5 – (-2) = 7

Question 5.
A variable that can assume any possible value between two points is called
(a) discrete random variable
(b) continuous random variable
(c) discrete sample space
(d) random variable
Solution:
(b) Continuous random Variable

Question 6.
A formula or equation used to represent the probability distribution of a continuous random variable is called
(a) probability distribution
(b) distribution function
(c) probability density function
(d) mathematical expectation
Solution:
(c) Probability density function

Question 7.
If X is a discrete random variable and p(x) is the probability of X, then the expected value of this random variable is equal to
(a) Σf(x)
(b) Σ[x + f(x)]
(c) Σf(x) + x
(d) Σxp(x)
Solution:
(d) Σxp(x)

Question 8.
Which of the following is not possible in probability distribution?
(a) Σp(x) > 0
(b) Σp(x) = 1
(c) Σxp(x) = 2
(d) p(x) = -0.5
Solution:
(d) P(x) = -0.5

Question 9.
If c is a constant, then E(c) is
(a) 0
(b) 1
(c) c f(c)
(d) c
Solution:
(d) c

Question 10.
A discrete probability distribution may be represented by
(a) table
(b) graph
(c) mathematical equation
(d) all of these
Solution:
(d) all of these

Question 11.
A probability density function may be represented by:
(a) table
(b) graph
(c) mathematical equation
(d) both (b) and (c)
Solution:
(d) both (b) and(c)

Question 12.
If c is a constant in a continuous probability distribution, then p(x = c) is always equal to
(a) zero
(b) one
(c) negative
(d) does not exist
Solution:
(a) Zero

Question 13.
E[X – E(X)] is equal to
(a) E(X)
(b) V(X)
(c) 0
(d) E(X) – X
Solution:
(c) 0

Question 14.
E[X – E(X)]² is
(a) E(X)
(b) E(X)²
(c) V(X)
(d) S.D(X)
Solution:
(c) V(X)

Question 15.
If the random variable takes negative values, then the negative values will have
(a) positive probabilities
(b) negative probabilities
(c) constant probabilities
(d) difficult to tell
Solution:
(a) Positive probabilities

Question 16.
If we have f(x) = 2x, 0 ≤ x ≤ 1, then f(x) is a
(a) probability distribution
(b) probability density function
(c) distribution function
(d) continuous random variable
Solution:
(b) Probability density function

Question 17.
$$\int_{ -∞ }^{∞}$$ f(x) dx is always equal to
(a) zero
(b) one
(c) E(X)
(d) f(x) + 1
Solution:
(b) one

Question 18.
A listing of all the outcomes of an experiment and the probability associated with each outcome is called
(a) probability distribution
(b) probability density function
(c) attributes
(d) distribution function
Solution:
(a) Probability distribution

Question 19.
Which one is not an example of random experiment ?
(a) A coin is tossed and the outcome is either a head or a tail
(b) A six-sided die is rolled
(c) Some number of persons will be admitted to a hospital emergency room during any hour.
(d) All medical insurance claims received by a company in a given year.
Solution:
(d) All medical insurance claims received by a company in a given year

Question 20.
A set of numerical values assigned to a sample space is called
(a) random sample
(b) random variable
(c) random numbers
(d) random experiment
Solution:
(b) random variable

Question 21.
A variable which can assume finite or countably infinite number of values is known as
(a) continuous
(b) discrete
(c) qualitative
(d) none of them
Solution:
(b) Discrete

Question 22.
The probability function of a random variable is defined as

Then k is equal to
(a) zero
(b) $$\frac { 1 }{4}$$
(c) $$\frac { 1 }{15}$$
(d) one
Solution:
(c) k = 1/15
Hint:
W.K.T Σi=1 P(xi) = 1
p(x= -1)+ p(x= -2) + p(x = 0) + p(x = 1)
+ p(x = 2) = V
k + 2k + 3k + 4k + 5k = 1
5k = 1 ⇒ k = 1/5

Question 23.
If p(x) = $$\frac { 1 }{10}$$, x = 10, then E(X) is
(a) zero
(b) $$\frac { 6 }{8}$$
(c) 1
(d) -1
Solution:
(c) 1
Hint:
P(x) + 1/10 and x = 10
E(x) = Xp(x) = 10(1/10) = 1

Question 24.
A discrete probability function p(x) is always
(a) non-negative
(b) negative
(c) one
(d) zero
Solution:
(a) non-negative

Question 25.
In a discrete probability distribution the sum of all the probabilities is always equal to
(a) zero
(b) one
(c) minimum
(d) maximum
Solution:
(b) one

Question 26.
An expected value of a random variable is equal to it’s
(a) variance
(b) standard deviation
(c) mean
(d) con variance
Solution:
(c) mean

Question 27.
A discrete probability function p(x) is always non-negative and always lies between
(a) 0 and ∞
(b) 0 and 1
(c) -1 and +1
(d) -∞ and ∞
Solution:
(b) 0 and 1

Question 28.
The probability density function p(x) cannot exceed
(a) zero
(b) one
(c) mean
(d) infinity
Solution:
(b) One

Question 29.
The height of persons in a country is a random variable of the type
(a) discrete random variable
(b) continuous random variable
(c) both (a) and (b)
(d) neither (a) not (b)
Solution:
(b) Continuous random variable

Question 30.
The distribution function F(x) is equal to
(a) P(X = x)
(b) P(X ≤ x)
(c) P (X ≥ x)
(d) all of these
Solution:
(b) p(x ≤ x)