Probability and Statistics Solved MCQs

1.

What is E(ax+b)?

A. ax+b,
B. ax,
C. aE(x),
D. aE(x)+b
Answer» D. aE(x)+b
2.

Write mean in term of moments?

A. µ1’,
B. µ2’,
C. µ2’- µ1’,
D. ( µ1’)2
Answer» A. µ1’,
3.

V(ax+b)= ………………..

A. ax+b,
B. aV(x)+b,
C. a2V(x)+b,
D. a2V(x)
Answer» D. a2V(x)
4.

The scatterness of observation is called ……………

A. Skewness,
B. Kurtosis,
C. Dispersion,
D. Mean
Answer» C. Dispersion,
5.

For leptokurtic distribution

A. β2 < 3,
B. β2 > 3,
C. β2= 3,
D. β2= 0
Answer» B. β2 > 3,
6.

Any measure calculated on the basis of population value is called ………

A. Parameter,
B. Statistic,
C. Sample,
D. Distribution
Answer» A. Parameter,
7.

Give the suitable expression for E(x-c)2

A. E(x2)-C2,
B. (E(x)-E(c))2,
C. V(x) + (E(x)-C)2,
D. V(x2)-C2
Answer» C. V(x) + (E(x)-C)2,
8.

The degree of relation between two variable is called

A. Correlation
B. Regression
C. Correlation Coefficient
Answer» A. Correlation
9.

Correlation coefficient lies between …………

A. 0 & 1,
B. -1 & 1,
C. -1 & 0,
D. -∞ & ∞
Answer» B. -1 & 1,
10.

If there is no relation between two variables correlation is called …………

A. Positive,
B. Zero,
C. Negative,
D. Normal
Answer» B. Zero,
11.

What is the maximum value of probability?

A. 1
B. zero
C. -1
D. 2
Answer» A. 1
12.

P (AUB) =?

A. P(A)+P(B)
B. P(A) U P(B)
C. P(A) - P(B)
D. P(A)+P(B)-P(A∩B)
Answer» D. P(A)+P(B)-P(A∩B)
13.

In which distribution means variance coincide?

A. Binomial
B. Poisson
C. Uniform
D. Normal
Answer» B. Poisson
14.

Binomial distribution is a ______ distribution?

A. Discrete
B. Continuous
C. Bivariate
Answer» A. Discrete
15.

_____ distribution is a limiting case of binomial?

A. Normal
B. Poisson
C. Uniform
D. Gamma
Answer» B. Poisson
16.

What is the mean of the binomial distribution?

A. n
B. p
C. np
D. npq
Answer» C. np
17.

If A & B are independent events which of the following are true

A. P(AUB)=P(A)+P(B)
B. P(A∩B)=P(A).P(B)
C. P(A/B)=P(A)/P(B)
D. P(A-B)=P(A)-P(B)
Answer» B. P(A∩B)=P(A).P(B)
18.

What is the MGF of Normal distribution?

A. (q+pet)n
B. e(et-1)
C. npq
D. eµt + t2 Ϭ2/2
Answer» D. eµt + t2 Ϭ2/2
19.

Find variance in terms of moments?

A. µ2! ,
B. µ1! ,
C. (µ1!)2
D. µ2! - (µ1!)2
Answer» D. µ2! - (µ1!)2
20.

If mean=median=mode in a distribution then which is called____________?

A. Binomial
B. Normal
C. Poisson
D. Uniform
Answer» B. Normal
21.

The degree to which numerical data tend to spread about an average value is

A. Mean,
B. Average,
C. Dispersion,
D. Mode
Answer» C. Dispersion,
22.

____________ =Q3-Q1/2

A. skewness,
B. Quartile deviation,
C. Mean deviation,
D. Range
Answer» B. Quartile deviation,
23.

Mean deviation is least when calculated from ________________

A. Mean,
B. Median,
C. Mode,
D. S.D
Answer» B. Median,
24.

If the varience is 256, then S.D is

A. 16,
B. 4,
C. 2,
D. 512
Answer» A. 16,
25.

S.D is a measure of ____________dispersion

A. Relative,
B. absolute,
C. Negative,
D. None of these
Answer» B. absolute,
26.

In a symmetrical distribution quartiles are equidistant from____________

A. Mean,
B. Median,
C. Mode,
D. S.D
Answer» B. Median,
27.

In a negatively skewed distribution,

A. Mean=Median=Mode,
B. Mode<Median<Mode,
C. Mode<Median<Mean,
D. Mean<Median<Mode
Answer» D. Mean<Median<Mode
28.

Karl Pearson coefficient of skewness does not depend on

A. Mean,
B. Median,
C. Mode,
D. First quartile
Answer» D. First quartile
29.

In a Binomial distribution varience is 4/3 and p(success) is 1/3 find mean?

A. 2,
B. 4,
C. 6,
D. 8
Answer» A. 2,
30.

Find the varience of the binomial distribution whose mgf is (0.4et+0.6)8

A. 1.92,
B. 0.92,
C. 0.24,
D. 7.86
Answer» A. 1.92,
31.

The standard deviation of the sampling distribution of a statistic is called

A. Standard error,
B. error,
C. population deviation,
D. population error
Answer» A. Standard error,
32.

What is the standard error of x?

A. Ϭ,
B. Ϭ2
C. Ϭ/√n
D. Ϭ2/n
Answer» C. Ϭ/√n
33.

What is the necessary condition for an estimator‘t’ is unbiased

A. t=0,
B. E(t)=0,
C. E(t)= ɵ,
D. t= ɵ
Answer» C. E(t)= ɵ,
34.

What is the condition that t1 is more efficient than t2

A. t1<t2,
B. E (t1) <E (t2),
C. V (t1) < V (t2),
D. t1>t2)
Answer» C. V (t1) < V (t2),
35.

The Rejected region in a statistical test is called ------------------------------

A. First type
B. Second type
C. critical
D. none of these
Answer» C. critical
36.

The estimator tn of parameter ɵ is consistent if tn converges to…………….. in probability

A. ɵ2,
B. ɵ,
C. 0,
D. 1
Answer» B. ɵ,
37.

A consistent estimator is unbiased if

A. Small sample,
B. large sample,
C. finite sample ,
D. countable sample
Answer» B. large sample,
38.

(V (t1) / V (t2) ) is called……………………

A. relative efficiency of t1 w.r.to t2
B. relative efficiency of t2 w.r.to t1
C. relative sufficiency of t1 w.r.to t2
D. relative sufficiency of t2 w.r.to t1
Answer» B. relative efficiency of t2 w.r.to t1
39.

the hypothesis against the null hypothesis is called ---------------------

A. zero
B. test
C. alternate
D. none of these
Answer» C. alternate
40.

probability of the test static falling in the critical region is called -----------

A. significance
B. rejected
C. statistical
D. none of these
Answer» A. significance
41.

In a normal distribution with mean µ and variance 1, t=1/nxi 2 is an unbiased estimator of ____________?

A. Ø
B. µ
C. µ2
D. µ2+1
Answer» D. µ2+1
42.

Sample mean is the consistent estimator of _____________?

A. population mean
B. Sample variance
C. Population variance
D. S.D
Answer» A. population mean
43.

If ‘t’ is consistent estimator of Q ,Then t2 is the consistent estimator of __________ ?

A. Q
B. Q2
Answer» B. Q2
44.

For the population f(x,µ)=1/ 2)

A. Sample mean is not a consistent estimator, but sample median is a consistent estimator
B. Sample median is not a consistent estimator, but sample mean is a consistent estimator
C. Sample variance is not a consistent estimator, but population variance is a consistent estimator
D. Sample variance is a consistent estimator, but population variance is not a consistent estimator
Answer» A. Sample mean is not a consistent estimator, but sample median is a consistent estimator
45.

The kurtosis ᵝ2 =__________?

A. µ4/µ2
B. µ4/µ1
C. µ4/µ22
D. µ4/µ12
Answer» C. µ4/µ22
46.

At t=0,Mx (t)=___________?

A. zero
B. 1
C. -1
D. 2
Answer» B. 1
47.

Which distribution is limiting case of binomial distribution as n->∞,p->0

A. Poisson
B. normal
C. uniform
D. gamma
Answer» A. Poisson
48.

In which distribution Mean=Median=Mode?

A. Poisson
B. normal
C. uniform
D. gamma
Answer» B. normal
49.

Variance of k, where k is a constant is

A. k2
B. k
C. zero
D. 1
Answer» C. zero
50.

Expectation of a constant k is

A. zero
B. 1
C. k
D. k2
Answer» C. k
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