If P(X=x)=0, then f(x) is a __________ probability function.

• A) Bivariate
• B) Discrete
• C) Univariate
• D) Continuous

Nature of the binomial random variable X is:

• A) Qualitative
• B) Continuous
• C) Quantitative
• D) Discrete

Which of the following is a major difference between the binomial and the hyper geometric distributions?

• A) The sum of the outcomes can be greater than 1 for the hyper geometric.
• B) The outcomes cannot be whole numbers in the hyper geometric distribution.
• C) The probability of a success changes from trial to trial in the hyper geometric distribution
• D) The number of trials changes in the hyper geometric distribution.

Parameters of hyper geometric distribution are:

• A) 1
• B) 3
• C) 5
• D) 2

Let X and Y be two independent random variables then E(XY) =

• A) 0
• B) 1
• C) E(X) E(Y)
• D) E(X)/ E(Y)

Var(2X + 6) =__________

• A) 2 var(x)
• B) 4 var(x)
• C) 16 var(x)
• D) 8 var(x)

A random variable that can assume every possible value in an interval [a, b]:

• A) Categorical variable
• B) Qualitative variable
• C) Continuous variable
• D) Discrete variable

The number of students waiting a bus stop in the morning and their probabilities are given below. Where x = number of students waiting at the bus stop.
x f(x)
0 0.10
1 0.25
2 0.30
3 0.20
4 0.15
What is the probability that there are 2 (x=2) students waiting at the bus stop?

• A) 0.15
• B) 0.25
• C) 0.30
• D) 0.0

Let $$f(X_i ,Y_i )$$ be the joint probability function of the two discrete random variables X and Y where i = 1,2,3,....,m and j = 1,2,3,....,n, then the marginal probability function of X is defined as:

• A) None of the above
• B) $$g(x_i ) = \sum\nolimits_j {f(X_i ,Y_i )}$$
• C) $$g(x_i ) = \sum\nolimits_i {f(X_i ,Y_i )}$$
• D) Both of the above

A random variable Y has the following probability distribution:
y: -1 0 1 2
P(y): 3C 2C 0.4 0.1

Calculate the of ‘C’

• A) 0.10
• B) 0.15
• C) 0.20
• D) 0.25

The number of parameters in normal distribution is(are):

• A) 4
• B) 2
• C) 1
• D) 3

It is sometimes possible to obtain approximate probabilities associated with values of a random variable by using the different probability distribution of a different random variable. For example, binomial probabilities use the Poisson probability function, binomial probabilities using the normal etc. In order for the Poisson to give “good” approximate values for binomial probabilities we must have the condition(s) that:

• A) The probability, p, is small and the sample size is large
• B) The probability, p, is close to 0.5 and the population size is large
• C) The population size is large relative to the sample size
• D) The probability, p, is close to 0.5 and the sample size is large

$${\text{In a normal distribution how much area lies between }}\mu \pm \sigma$$

• A) 80%
• B) 75%
• C) 65%
• D) 68.26%

E(3X + 5) = ?

• A) E3(X) + 5.
• B) 3 E(X) + 5.
• C) 3 E(X) .
• D) 3(X) + 5.

P[(X+Y) < 2] =? , where x=0, 1, 2 and y=0, 1, 2

• A) f(0,0) + f(1,1) + f(2,0)
• B) f(0,0) + f(1,1) + f(1,0)
• C) f(0,0) + f(0,1) + f(1,0)
• D) f(0,1) + f(0,2) + f(2,0)

A sales firm receives different calls from clients. If someone says, today it will receive “at least 3 calls”. How many calls will be received?

• A) 3, 4, 5, . . .
• B) 0, 1, 2, 3, 5, . . .
• C) 1, 2, 3
• D) 0, 1, 2, 3

The mean deviation of the normal distribution is approximately:

• A) 3/4 of the S.D
• B) 7/8 of the S.D
• C) 1/2 of the S.D
• D) 4/5 of the S.D

If µ3 = 3 and µ2 = 2 then the skewness of the distribution will be:

• A) 0.87
• B) 1.5
• C) 2.5
• D) 1.125

If f(x) is a continuous probability function, then P(X = 2) is:

• A) 0
• B) 1
• C) 2
• D) 1/2

In a bivariate distribution f(x,y), when one random variable is discrete and the other is continuous, then we may call it __________ ?

• A) Co-discrete distribution
• B) Paired distribution
• C) Mixed distribution
• D) Matching distribution