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

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

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

Given E(X)=5 and E(Y)=−2, then E(X−Y) is ________.

(a)

3

(b)

5

(c)

7

(d)

-2

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

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

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)

\(\sum { f(x) } \)

(b)

\(\sum[x+f(x)]\)

(c)

\(\sum { f(x)+x } \)

(d)

\(\sum { xp(x) } \)

Which of the following is not possible in probability distribution?

(a)

\(\sum { p(x)\ge 0 } \)

(b)

\(\sum { p(x)=1 } \)

(c)

\(\sum { xp(x)=2 } \)

(d)

\(p(x)=-0.5\)

If c is a constant, then E(c) is ________.

(a)

0

(b)

1

(c)

c f (c)

(d)

c

A discrete probability distribution may be represented by ________.

(a)

table

(b)

graph

(c)

mathematical equation

(d)

all of these

A probability density function may be represented by ________.

(a)

table

(b)

graph

(c)

mathematical equation

(d)

both (b) and (c)

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

E[X-E(X)] is equal to ________.

(a)

E(X)

(b)

V(X)

(c)

0

(d)

E(X)-X

E[X-E(X)]² is ________.

(a)

E(X)

(b)

E(X²)

(c)

V(X)

(d)

S.D(X)

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

If we have f(x)=2x, 0\(\le\)x\(\le\)1, then f (x) is a ________.

(a)

probability distribution

(b)

probability density function

(c)

distribution function

(d)

continuous random variable

\(\int _{ -\infty }^{ \infty }{ f(x)dx } \) is always equal to ________.

(a)

zero

(b)

one

(c)

E(X)

(d)

f(x)+1

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

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

A set of numerical values assigned to a sample space is called ________.

(a)

random sample

(b)

random variable

(c)

random numbers

(d)

random experiment

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

The probability function of a random variable is defined as

X=x	-1	-2	0	1	2
P(x)	K	2K	3K	4K	5K

Then k is equal to ________.

(a)

zero

(b)

\(\frac{1}{4}\)

(c)

\(\frac{1}{15}\)

(d)

one

If p(x) =\(\frac{1}{10}\), c = 10, then E(X) is ________.

(a)

zero

(b)

\(\frac{6}{8}\)

(c)

1

(d)

-1

A discrete probability function p(x) is always ________.

(a)

non-negative

(b)

negative

(c)

one

(d)

zero

In a discrete probability distribution the sum of all the probabilities is always equal to ________.

(a)

zero

(b)

one

(c)

minimum

(d)

maximum

An expected value of a random variable is equal to it’s ________.

(a)

variance

(b)

standard deviation

(c)

mean

(d)

covariance

A discrete probability function p(x) is always non-negative and always lies between ________.

(a)

0 and \(\infty \)

(b)

0 and 1

(c)

–1 and +1

(d)

–∞ and +∞

The probability density function p(x) cannot exceed ________.

(a)

zero

(b)

one

(c)

mean

(d)

infinity

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) nor (b)

The distribution function F(x) is equal to ________.

(a)

\(P(X=x)\)

(b)

P(X\(\le\)x)

(c)

P(X\(\ge\)x)

(d)

all of these