This section contains Multiple Choice Questions about Measure of Probability, Probability Rules, Conditional Probability, Bays Theorem, Probability Distributions, Discrete and Continuous Probability Distributions etc

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Question 1

Which of the following is not a condition of the binomial distribution?

A

Only 2 possible outcomes

B

have constant probability of success

C

must have at least 3 trials

D

trials must be independent

Question 2

Which of the following is not a correct statement about a probability.

A

It must have a value between 0 and 1

B

It can be reported as a decimal or a fraction

C

A value near 0 means that the event is not likely to occur/happens

D

It is the collection of several experiments.

Question 2 Explanation:

Probability is measure of uncertainty its not collection of several experiments.

Question 3

If the occurrence of one event means that another cannot happen, then the events are

A

Independent

B

Mutually Exclusive

C

Bayesian

D

Empirical

Question 3 Explanation:

Two events are mutually exclusive if they (both of them) cannot occur together.

Question 4

A listing of the possibile outcomes of an experiment and their corresponding probability is called

A

Random Variable

B

Contingency table

C

Bayesian table

D

Probability distribution

E

Frequency distribution

Question 4 Explanation:

Probability distribution is listing of the all possible outcomes from an experiment with their associated probability for each outcome.

Question 5

Which of the following is not an example of a discrete probability distribution?

A

The sale or purchase price of a house

B

The number of bedrooms in a house

C

The number of bathrooms in a house

D

Whether or not a home has a swimming pool in it.

Question 6

In which approach to probability the outcomes are equally likely to occur?

A

Classical Probability

B

Subjective Probability

C

Relative Frequency

D

Independent

Question 6 Explanation:

In Classical probability the outcomes are equally likely to occur.

Question 7

If you roll a pair of dice, what is the probability that (at least) one of the dice is a 4 or the sum of the dice is 7?

A

4/36

B

13/36

C

21/36

D

15/36

Question 7 Explanation:

These are the possibilities of the required event to occur.
{(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (5,4), (6,4), (1,6), (2,5), (3, 4), (5,2), (6,1)}

Question 8

The joint probability is

A

The likelihood of two events happening together

B

The likelihood of an event happening given that another event has already happened

C

Based on two mutually exclusive events

D

Also called Prior probability

Question 8 Explanation:

Joint probability is the joint occurrence of one or more events

Question 9

The collection of one or more outcomes from an experiment is called

A

Probability

B

Event

C

Random Variable

D

Z-Value

E

Random Experiment

Question 9 Explanation:

An event is collection of one or more outcomes from an experiment.

Question 10

In special rule of addition of probability, the events are always

A

Independent events

B

Mutually Exclusive events

C

Bayesian

D

Empirical

Question 10 Explanation:

In special rule of addition of probability the events must be mutually exclusive.

Question 11

If a card is chosen from a standard deck of cards, what is the probability of getting a diamond (♦) or a club(♣)?

A

26/52=1/2

B

13/52

C

20/52

D

12/52

Question 11 Explanation:

There are 13 cards of club and 13 card of diamond. Addition rule is used here

Question 12

If a card is chosen from a standard deck of cards, what is the probability of getting a five or a seven?

A

4/52

B

1/26

C

8/52

D

1/169

Question 13

The the special rule of multiplication of probability, the events must be

A

Independent

B

Mutually exclusive

C

Bayesian

D

Empirical

Question 13 Explanation:

If two events are independent, i.e. are not related, the special rule of multiplication is used to fined the probability of their joint occurrence. P(A and B)=P(A) x P(B)

Question 14

In a Poisson probability distribution

A

The mean and variance of the distribution are same (equal)

B

The probability of success is always greater than 5

C

The number of trials is always less than 5

D

It always contains a contingency table

Question 14 Explanation:

The mean and variance in Poisson distribution is always same.

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Question 1

If in a binomial distribution n = 1 then E(X) is

A

q

B

p

C

0

D

1

Question 2

Binomial distribution is negatively skewed when

A

p=0

B

p>1/2

C

p<1/2

D

p=-1/2

E

p=1/3

Question 2 Explanation:

If p<0.5, then the distribution is positively skewed; if p>0.5, the distribution is negatively skewed.

Question 3

The mean of hypergeometric distribution is

A

$\frac{nk}{N}$

B

$\frac{N-k}{n}$

C

$\frac{nN}{k}$

D

$\frac{n+k}{N}$

Question 4

The probability of success changes from trial to trial in

A

Binomial distribution

B

Geometric distribution

C

Sampling distribution

D

Hypergeometric distribution

Question 5

A random variable X has binomial distribution with n = 10 and p = 0.3 then variance of X is

A

10

B

12

C

2.1

D

21

E

None

Question 6

A fair coin is tossed four times, the probability of getting four heads is

A

1/4

B

1/2

C

1/16

D

1

E

0

Question 6 Explanation:

here n=4, x=4, p=q=0.5

Question 7

The successive trials are with replacement in

A

Hypergeometric distribution

B

Binomial distribution

C

Geometric distribution

D

None of above

Question 8

Which of the following is not the property of binomial distribution

A

n is fixed

B

has two outcomes

C

Trials are independent

D

Probability of success varies from trial to trial

Question 9

The mean of binomial distribution is

A

npq

B

np

C

$\sqrt{npq}$

D

$\sqrt{np}$

E

$\sqrt{nq}$

Question 10

The mean, median and mode for binomial distribution will be equal when

A

p =0.5

B

p< 0.5

C

p> 0.5

D

p= 1

E

None of these

Question 11

Hypergeometric distribution has parameters

A

2

B

1

C

3

D

4

E

No

Question 12

In hypergeometric distribution, the trials are

A

Independent

B

Dependent

C

Collectively Exhaustive

D

None

Question 13

In which distribution successive trials are without replacement

A

Hypergeometric distribution

B

Binomial distribution

C

Poisson distribution

D

Geometric distribution

Question 14

The variance of binomial distribution is always

A

Less than mean

B

Equal to mean

C

Greater than mean

D

Equal to standard deviation

E

None of these

Question 14 Explanation:

In other words mean of binomial distribution is always greater than variance.

Question 15

In a binomial probability distribution it is impossible to find

A

P(X < 0)

B

P(X = 0)

C

P(X > 0)

D

P(0 ≤ X ≤ n)

Question 16

Successive trials in binomial distribution are

A

Dependent

B

Independent

C

Equally Likely

D

Mutually exclusive

E

None

Question 17

Binomial distribution is symmetrical when

A

p = q

B

p > q

C

p < q

D

np > npq

Question 18

In binomial distribution n=6 and p=0.9, then the value of P(X=7) is

A

One

B

Less than zero

C

Zero

D

More than zero

Question 19

Binomial distribution has parameters

A

Three

B

Two

C

One

D

Four

E

None

Question 20

Each trial in Binomial distribution has

A

One Outcome

B

Two Outcome

C

Three Outcome

D

Four Outcome

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Test 3

MCQs on Discrete Probability Distribution and Distribution Function III

This test contains more MCQs about probability and probability distribution. All of the MCQs are from Discrete Probability Distribution and Distribution Function

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Question 1

A discrete probability distribution may be represented by

A

A table

B

A graph

C

A mathematical Equation

D

All of these

Question 2

For a probability density function (pdf), the probability of a single point is

A

1

B

2

C

0

D

Constant

Question 3

Probability of occurrence of an event lies between

A

-1 and 0

B

0 and 1

C

-1 and 1

D

exactly 1

Question 4

If C is non-random variable, the E(C) is

A

Zero

B

C

C

1

D

2

E

None

Question 5

For a random variable X, E(X) is

A

Harmonic Mean (HM)

B

Geometric Mean (GM)

C

Arithmetic Mean (AM)

D

Non

Question 6

For distribution Function F(X), $F(-\infty)=0$ and $F(\infty)=$?

A

0

B

-1

C

1

Question 7

Probability distribution of a random variable is also known as

A

Probability

B

Probability Function

C

Distribution Function

D

Probability Distribution

E

Probability Density Function

Question 8

Total Area under the curve in probability of density function is

A

0

B

-1

C

1

D

Infinity

Question 9

The probability function is always

A

Negative

B

Non Negative

C

Positive

D

None

Question 10

The distribution function F(X) is represented by

A

P(X=x)

B

P(X

C

P(X>x)

D

$P(X\le x)$

Question 11

What is the probability that a ball drawn at random from a jar?

A

0.1

B

1

C

0.5

D

0

E

Cannot be determined from given information

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Test 4

MCQs on Normal Probability Distribution IV

This Multiple Choice Questions test is based on Normal Probability Distribution, which includes its mean, median, mode, Variance, Standard Normal Distribution etc. All this will help you to understand the properties and characteristics of Normal Distribution and It will also help to to pass examination of school, college or and competitive exams.
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Question 1

The Normal Curve is asymptotic to the

A

None

B

X-axis

C

Along Y=X

D

Y-axis

Question 2

The lower and upper quartiles of standard normal variate are respectively

A

-0.6745 and 0.6745

B

$-0.7979\sigma$ and $0.7979 \sigma$

C

-0.7979 and 0.7979

D

$\mu+0.6745\sigma$ and $\mu-0.6745\sigma$

Question 3

Mean deviation of Normal Distribution is

A

$\frac{7}{8}\sigma$

B

$\frac{2}{3}\sigma$

C

$\frac{4}{5}\sigma$

D

$\frac{3}{4}\sigma$

Question 4

Which of the following parameter control the relative flatness of normal distribution

A

Standard Deviation

B

Mean

C

Mode

D

None

Question 5

Normal Distribution

A

Bi Modal

B

Uni Modal

C

Tri Modal

D

Have no Mode

E

Multi Modal

Question 6

The Normal Distribution has parameters

A

3

B

4

C

2

D

1

Question 7

If X~N(16, 49), then mean is

A

7

B

16

C

4

D

49

Question 8

The median of normal distribution corresponds to the value of Z equal to

A

$\mu$

B

0

C

0.5

D

1

Question 9

Total Area under the normal curve is

A

Greater than 1

B

Less than 1

C

0

D

None

E

1

Question 10

If Y=5X + 10 and X is N(10,25), then mean of Y is

A

135

B

60

C

70

D

50

Question 11

In Normal distribution, the parameters which controls the flatness of the curve is

A

$\mu, MD$

B

$\sqrt{2\pi},e$

C

$\mu,\sigma$

D

None

Question 12

In case of symmetrical distribution

A

$\beta_1 =\beta_4$

B

$\mu_3=\mu_4$

C

Mean=Mode=Median

D

$\mu_1 = \mu_2$

Question 13

Normal Distribution is

A

PLatykurtic

B

Leptokurtic

C

Mesokurtic

D

None

Question 14

The shape of normal curve depends upon

A

None

B

Mean Deviation

C

Quartile Deviation

D

Standard Deviation

E

Mean

Question 15

Shape of normal curve can be related to

A

Bell

B

L

C

J

D

Rectangle

E

Circle

Question 16

In a normal distribution $E(X-\mu)^2$ is

A

Mean Deviation

B

Quantile Deviation

C

Standard Deviation

D

Variance

Question 17

We use normal distribution when "n" is

A

Large

B

Fixed

C

None

D

Small

Question 18

If $X~N(55,49)$ then $\sigma$

A

55

B

7

C

49

D

104

Question 19

Area under the normal curve on either side of mean is

A

Mean value

B

2

C

-1

D

1

E

0.5

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Test 5

MCQS on Variable and Random Variable

This section contains MCQS on variable and Random variable. This includes some definitions, examples and type of random variable. Please keep visiting and sharing for promoting the site http://itfeature.com.

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The Z-Score The Z-score also referred to as standardized raw scores is a useful statistic because not only permits to compute the probability (chances or likelihood) of raw score (occurring within normal distribution) but also it helps to compare two raw scores from different normal distributions. The Z-score is a dimensionless measure since it is […]

Multicollinearity in Linear Regression Models The objective of multiple regression analysis is to approximate the relationship of individual parameters of a dependency, but not of interdependency. It is assumed that the dependent variable and regressors ‘s are linearly related to each other (Graybill, 1980; Johnston, 1963 and Malinvaud, 1968). Therefore, inferences depicted from any regression […]

Levels of Measurement (Scale of Measure) Level of measurement (scale of measure) have been classified into four categories. It is important to understand these level of measurement, since these level of measurement play important part in determining the arithmetic and different possible statistical tests that are carried on the data. The scale of measure is […]

Variance is a measure of dispersion of a distribution of a random variable. The term variance was introduced by R. A. Fisher in 1918. The variance of a set of observations (data set) is defined as the mean of the squares of deviations of all the observations from their mean. When it is computed for […]

A research can be classified into two groups: Qualitative and Quantitative Research Qualitative Research Qualitative research involves collecting data from in-dept interviews, observations, field notes, and open-ended questions in questionnaire etc. The researcher himself is the primary data collection instrument and the data could be collected in form of words, images, and patterns etc.For Qualitative […]

In R language, list is an object that consists of an ordered collection of objects known as its components. A list in R Language is a structured data that can have any number of any modes (types) of other structured data. That is, one can put any kind of object (like vector, data frame, character …

The R program’s structure is similar to the programs written in other computer languages such as C or its successors C++ and Java. However, important differences between these languages and R are (i) R has no header files, (ii) most of the declarations are implicit, (iii) there are no pointers in R, and (iv) text …

The problem of multicollinearity plagues the numerical stability of regression estimates. It also causes some serious problem in validation and interpretation of the regression model. Consider the usual multiple linear regression model, , where is an vector of observation on dependent variable, is known design matrix of order , having full-column rank , is vector of …

R language provides an interlocking suite of facilities that make fitting statistical models very simple. The output from statistical models in R language is minimal and one needs to ask for the details by calling extractor functions. Defining Statistical Models; Formulae in R Language The template for a statistical model is a linear regression model …

Source Code of R Method There are different ways to view the source code of an R method or function. It will help to know how function is working. Internal Functions If you want to see the source code of internal function (functions from base packages), just type the name of the function at R prompt such …

Question: How one can include Greek letter (symbols) in R plot labels? Answer: Greek letters or symbols can be included in titles and labels of graph using the expression command. Following are some examples Note that in these example random data is generated from normal distribution. You can use your own data set to produce …

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sir q#7 ka ans galat hai….sawal mai to deck of cards hai or ans mai pair of dice….check it plz

correction is made. Please whenever anyone found error do contact with test number and initial statement, so that I can easily search and correct the problem.

sir q#19 mai b problem hai…. check it out too…..agar symetric ka concern p se hai to explanation mai n q dia hua hai ?? plz clear it

can you send the statement of question, it will be easy for me to find. In test all questions and even there answers are randomly displayed.

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nice practice . thanks a lot

Great MCQS of Statistic for NTS Test, PPSC

very nice

Excellent input provided to strengthen the concepts. Thanks a lot

nice work. pl give a book of mcqs. Prof ramzan from khi

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good effort