Mathematical statistics

Final exam marks:60

MCQS (50)

1. When each outcome of a sample space is as likely to occur as any other, the outcomes are
called:
(a) Exhaustive
(b) Mutually exclusive
(c) Equally likely
(d) Not mutually exclusive
2. If an event contains more than one sample points, it is called a:
(a) Simple event
(b) Compound event
(c) Impossible event
(d) Certain event
3. An arrangement in which the order of the objects selected from a specific pool of objects is
important called:
(a) Combination
(b) Permutation
(c) Factorial
(d) Sample space
4. Three books of different colours are to be arranged in a book-shelf. The possible arrangements
are:
(a) 3
(b) 1
(c) 6
(d) 2
5. 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
6. Given E(X) = 5 and E(Y) = -2, then E(X - Y) is:
(a) 3
(b) 5
(c) 7
(d)10
7. E[X - E(X)] is equal to:
(a) E(X)
(b) Var(X)
(c) 0
(d) E(X) – X
+∞
8. ∫−∞ 𝑓(𝑥)𝑑𝑥 =?
(a) Zero
(b) One
 Mathematical statistics
Final exam marks:60

(c) E(X)
(d) f(x) + 1
9. Var( 4X + 8) is:
(a) 12 Var(X)
(b) 4 Var(X)+8
(c) 16 Var(X)
(d) 16 Var(X)+8
10. In a Binomial Distribution, if p = q, then P(X = x) is given by?
a) nCx (0.5)n
b) nCn (0.5)n
c) nCx p(n-x)
d) nCn p(n-x)
11. If Var(x-y)=? Then
a) a. Var(x)+Var(y)
b) b. Var(x)-Var(y)
c) c. a. Var(x)*Var(y)
d) d. None of these

12. What is the area under a conditional Cumulative density function?

a) 0
b) Infinity
c) 1
d) Changes with CDF
13. Out of the following values, which one is not possible in probability?
a) P(x) = 1
b) ∑ x P(x) = 3
c) P(x) = 0.5
d) P(x) = – 0.5
14. Let X be the number of heads obtained in 40 independent tosses of a fair coin. Then X is a
Binomial random variable with (a) n = 40, p = 0. (b) n = 0.5, p = 40. (c) n = 40, p = 0.5. (d) n = 100,
p = 0.
15. What is variance of a geometric distribution having parameter p=0.72?
a) 54%
b) 76%
c) 13%
d) 69%
16. . If the standard deviation of a population is 50 and the sample size is 16 then the
standard deviation of the sampling distribution is ________
a) 12.5
b) 12.25
c) 13.25
d) 14.25
 Mathematical statistics
Final exam marks:60
17. Sampling error increases as we increase the sampling size.
a) True
b) False
18. The difference between the sample value expected and the estimates value of the
parameter is called as?
a) bias
b) error
c) contradiction
d) difference
19. Which of the following is a subset of population?
a) distribution
b) sample
c) data
d) set
20. A bag contains 6 balls of different colours. A student selects 2 balls at random
without replacement. Find all possible combinations of the colours of the selected
balls.
a) 13
b) 14
c) 15
d) 16
21. A population has 10 items and a sample has been selected from it containing 5
items. Find the finite population correction factor.
a) (5/8)1/2
b) (5/7)1/2
c) (5/9)1/2
d) (5/6)1/2
22. If the mean of population is 29 then the mean of sampling distribution is __________
a) 29
b) 30
c) 21
d) 31

23. A sample size is considered large in which of the following cases?

a) n > or = 30
b) n > or = 50
c) n < or = 30
d) n < or = 50

24. What is the mean of a Chi Square distribution with 6 degrees of freedom?
a) 4
b) 12
c) 6
d) 8
25. Which of the following is defined as the rule or formula to test a Null Hypothesis?
a) Test statistic
 Mathematical statistics
Final exam marks:60
b) Population statistic
c) Variance statistic
d) Null statistic
26. Mean of a random variable X is given by _________
a) E(X)
b) E(X2)
c) E(X ) – (E(X))2
2

d) (E(X))2
27. Variance of a constant ‘a’ is _________
a) 0
b) a
c) a/2
d) 1
28. E(X) = λ is for which distribution?
a) Bernoulli’s
b) Binomial
c) Poisson’s
d) Normal
29. In a Binomial Distribution, if ‘n’ is the number of trials and ‘p’ is the probability of
success, then the mean value is given by ___________
a) np
b) n
c) p
d) np(1-p)
30. In a Binomial Distribution, the mean and variance are equal.
a) True
b) False

31. The mean of hypergeometric distribution is _____________

a) n*k / N-1
b) n*k-1 / N
c) n-1*k / N
d) n*k / N

32. The probability of success and failures in hypergeometric distribution is not fixed.
a) True
b) False
33. Find the Variance of a Hypergeometric Distribution such that the probability that a 3-
trial hypergeometric experiment results in exactly 2 successes, when the population
consists of 7 items.
a) 0.6212
b) 0.6612
c) 0.6112
d) 0.612
34. If ‘m’ is the mean of a Poisson Distribution, then variance is given by ___________
a) m2
b) m⁄ 1
2

c) m
 Mathematical statistics
Final exam marks:60
d) m⁄
2

35. Normal Distribution is applied for ___________

a) Continuous Random Distribution
b) Discrete Random Variable
c) Irregular Random Variable
d) Uncertain Random Variable

36. The area under a standard normal curve is?

a) 0
b) 1
c) ∞
d) not defined
37. In Normal distribution, the highest value of ordinate occurs at ___________
a) Mean
b) Variance
c) Extremes
d) Same value occurs at all points
38. The value of constant ‘e’ appearing in normal distribution is ___________
a) 2.5185
b) 2.7836
c) 2.1783
d) 2.7183
39. In Standard normal distribution, the value of mode is ___________
a) 2
b) 1
c) 0
d) Not fixed
40. The mean of exponential distribution is given as __________
a) 1/λ
b) λ
c) λ2
d) 1/λ2

41. The mean and the variance for gamma distribution are __________
a) E(X) = 1/λ, Var(X) = α/λ2
b) E(X) = α/λ, Var(X) = 1/λ2
c) E(X) = α/λ, Var(X) = α/λ2
d) E(X) = αλ, Var(X) = αλ2

42. Putting α=1 in Gamma distribution results in _______

a) Exponential Distribution
b) Normal Distribution
c) Poisson Distribution
d) Binomial Distribution

43. What does the central limit theorem state?

a) if the sample size increases sampling distribution must approach normal
distribution
 Mathematical statistics
Final exam marks:60
b) if the sample size decreases then the sample distribution must approach normal
distribution
c) if the sample size increases then the sampling distribution much approach an
exponential distribution
d) if the sample size decreases then the sampling distribution much approach an
exponential distribution

44. The sampling error is defined as?

a) difference between statistic and parameter
b) difference between sample and parameter
c) difference between population and sample
d) difference between parameter and sample
45. Any population which we want to study is referred as?
a) standard population
b) final population
c) infinite population
d) target population
46. Selection of a football team for FIFA World Cup is called as?
a) random sampling
b) systematic sampling
c) purposive sampling
d) cluster sampling
47. The cluster sampling, stratified sampling or systematic samplings are types of
________
a) direct sampling
b) indirect sampling
c) random sampling
d) non random sampling
48. Find the population proportion p for an IPL team having total 30 players with 10
overseas players.
a) 1/2
b) 1/3
c) 2/3
d) 1/4
49. It is provided that for a sampling distribution E(X)=11 and ϕ=13. Find the bias in the
sampling.
a) 2
b) 4
c) 6
d) 3

50. The point where the Null Hypothesis gets rejected is called as?
a) Significant Value
b) Rejection Value
c) Acceptance Value
d) Critical Value