Probability and Statistics Solved MCQs

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1.	What is E(ax+b)?
A.	ax+b,
B.	ax,
C.	aE(x),
D.	aE(x)+b
Answer» D. aE(x)+b

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2.	Write mean in term of moments?
A.	µ1’,
B.	µ2’,
C.	µ2’- µ1’,
D.	( µ1’)2
Answer» A. µ1’,

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3.	V(ax+b)= ………………..
A.	ax+b,
B.	aV(x)+b,
C.	a2V(x)+b,
D.	a2V(x)
Answer» D. a2V(x)

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4.	The scatterness of observation is called ……………
A.	Skewness,
B.	Kurtosis,
C.	Dispersion,
D.	Mean
Answer» C. Dispersion,

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5.	For leptokurtic distribution
A.	β2 < 3,
B.	β2 > 3,
C.	β2= 3,
D.	β2= 0
Answer» B. β2 > 3,

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6.	Any measure calculated on the basis of population value is called ………
A.	Parameter,
B.	Statistic,
C.	Sample,
D.	Distribution
Answer» A. Parameter,

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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,

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8.	The degree of relation between two variable is called
A.	Correlation,
B.	Regression,
C.	Correlation Coefficient
Answer» B. Regression,

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9.	Correlation coefficient lies between …………
A.	0 & 1,
B.	-1 & 1,
C.	-1 & 0,
D.	-∞ & ∞
Answer» B. -1 & 1,

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10.	If there is no relation between two variables correlation is called …………
A.	Positive,
B.	Zero,
C.	Negative,
D.	Normal
Answer» B. Zero,

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11.	What is the maximum value of probability?
A.	1
B.	zero
C.	-1
D.	2
Answer» B. zero

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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)

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13.	In which distribution means variance coincide?
A.	Binomial
B.	Poisson
C.	Uniform
D.	Normal
Answer» B. Poisson

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14.	Binomial distribution is a ______ distribution?
A.	Discrete
B.	Continuous
C.	Bivariate
Answer» A. Discrete

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15.	_____ distribution is a limiting case of binomial?
A.	Normal
B.	Poisson
C.	Uniform
D.	Gamma
Answer» B. Poisson

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16.	What is the mean of the binomial distribution?
A.	n
B.	p
C.	np
D.	npq
Answer» C. np

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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)

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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

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19.	Find variance in terms of moments?
A.	µ2! ,
B.	µ1! ,
C.	(µ1!)2
D.	µ2! - (µ1!)2
Answer» D. µ2! - (µ1!)2

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20.	If mean=median=mode in a distribution then which is called____________?
A.	Binomial
B.	Normal
C.	Poisson
D.	Uniform
Answer» B. Normal

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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,

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22.	____________ =Q3-Q1/2
A.	skewness,
B.	Quartile deviation,
C.	Mean deviation,
D.	Range
Answer» B. Quartile deviation,

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23.	Mean deviation is least when calculated from ________________
A.	Mean,
B.	Median,
C.	Mode,
D.	S.D
Answer» B. Median,

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24.	If the varience is 256, then S.D is
A.	16,
B.	4,
C.	2,
D.	512
Answer» A. 16,

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25.	S.D is a measure of ____________dispersion
A.	Relative,
B.	absolute,
C.	Negative,
D.	None of these
Answer» B. absolute,

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26.	In a symmetrical distribution quartiles are equidistant from____________
A.	Mean,
B.	Median,
C.	Mode,
D.	S.D
Answer» B. Median,

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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

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28.	Karl Pearson coefficient of skewness does not depend on
A.	Mean,
B.	Median,
C.	Mode,
D.	First quartile
Answer» D. First quartile

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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,

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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,

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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,

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32.	What is the standard error of x?
A.	Ϭ,
B.	Ϭ2
C.	Ϭ/√n
D.	Ϭ2/n
Answer» C. Ϭ/√n

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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,

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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),

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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

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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,

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37.	A consistent estimator is unbiased if
A.	Small sample,
B.	large sample,
C.	finite sample ,
D.	countable sample
Answer» B. large sample,

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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

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39.	the hypothesis against the null hypothesis is called ---------------------
A.	zero
B.	test
C.	alternate
D.	none of these
Answer» C. alternate

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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

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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

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42.	Sample mean is the consistent estimator of _____________?
A.	population mean
B.	Sample variance
C.	Population variance
D.	S.D
Answer» A. population mean

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43.	If ‘t’ is consistent estimator of Q ,Then t2 is the consistent estimator of __________ ?
A.	Q
B.	Q2
Answer» B. Q2

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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

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45.	The kurtosis ᵝ2 =__________?
A.	µ4/µ2
B.	µ4/µ1
C.	µ4/µ22
D.	µ4/µ12
Answer» C. µ4/µ22

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46.	At t=0,Mx (t)=___________?
A.	zero
B.	1
C.	-1
D.	2
Answer» B. 1

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47.	Which distribution is limiting case of binomial distribution as n->∞,p->0
A.	Poisson
B.	normal
C.	uniform
D.	gamma
Answer» A. Poisson

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48.	In which distribution Mean=Median=Mode?
A.	Poisson
B.	normal
C.	uniform
D.	gamma
Answer» B. normal

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49.	Variance of k, where k is a constant is
A.	k2
B.	k
C.	zero
D.	1
Answer» C. zero

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50.	Expectation of a constant k is
A.	zero
B.	1
C.	k
D.	k2
Answer» C. k

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Probability and Statistics Solved MCQs

What is E(ax+b)?

Write mean in term of moments?

V(ax+b)= ………………..

The scatterness of observation is called ……………

For leptokurtic distribution

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

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

The degree of relation between two variable is called

Correlation coefficient lies between …………

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

What is the maximum value of probability?

P (AUB) =?

In which distribution means variance coincide?

Binomial distribution is a ______ distribution?

_____ distribution is a limiting case of binomial?

What is the mean of the binomial distribution?

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

What is the MGF of Normal distribution?

Find variance in terms of moments?

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

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

____________ =Q3-Q1/2

Mean deviation is least when calculated from ________________

If the varience is 256, then S.D is

S.D is a measure of ____________dispersion

In a symmetrical distribution quartiles are equidistant from____________

In a negatively skewed distribution,

Karl Pearson coefficient of skewness does not depend on

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

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

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

What is the standard error of x?

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

What is the condition that t1 is more efficient than t2

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

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

A consistent estimator is unbiased if

(V (t1) / V (t2) ) is called……………………

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

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

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

Sample mean is the consistent estimator of _____________?

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

For the population f(x,µ)=1/ 2)

The kurtosis ᵝ2 =__________?

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

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

In which distribution Mean=Median=Mode?

Variance of k, where k is a constant is

Expectation of a constant k is