A value of standard deviation is equal to 0, means

• A) Both above
• B) All the values are constant
• C) All the values in data are changing rapidly
• D) None of the above

What will be the value of C.V if S.D = 0.5 and mean = 1.

• A) 30%
• B) 50%
• C) 45%
• D) 10%

The uni-variate distribution obtained from a bi-variate distribution is known as:

• A) Joint Distribtion
• B) Both of the above
• C) None of the above
• D) Marginal Distribtion

$$\begin{gathered} {\text{If X and Y are two discrete r}}{\text{.v's with joint probability function f (X}}_i ,Y_j ), \ {\text{then the conditional distribution of X given Y is:}} \\ \end{gathered}$$ given by

• A) $$f\left( {{\text{X}}_i |Y_j } \right){\text{ }} = f\left( {X_i ,{\text{ Y}}_j } \right){\text{ }}/g\left( {X_i } \right)$$
• B) $$f\left( {{\text{X}}_i |Y_j } \right){\text{ }} = f\left( {X_i ,{\text{ Y}}_j } \right){\text{ }}/h\left( {Y_j } \right)$$
• C) None of the above
• D) Both of the above

The variance of the Hypergeometric distribution is:

• A) npq
• B) {nk(N-n)}/N(N-1)
• C) pq
• D) {nk(N-k)(N-n)}/N*N(N-1)

What range of limit to be used for INTEGRATION of joint p.d.f to obtain its marginal pdf?

• A) 0 to 1
• B) -1 to 1
• C) 0 to + ∞
• D) -∞ to +∞

Which of the following is NOT a requirement of a binomial distribution?

• A) A fixed number of trials
• B) Only two possible outcomes
• C) A constant probability of success
• D) Equally likely outcomes

Let X be a continuous random variable with probability density function f(x) and cumulative distribution function F(x). Then for any two numbers a and b with a<b, which of the following inequalities is true?

• A) P(a<=X<=b)=F(a)-F(b)
• B) P(X>a)=1-P(X<=a)
• C) F(x)=(x-a)/(b-a)
• D) P(X>b)=F(b)-1

The location and shape of the normal curve is (are) determined by:

• A) Mean & standard deviation
• B) Mean & variance
• C) Variance
• D) Mean

If b(x, 15, 0.70), the variance of this distribution is

• A) 3.51
• B) 3.15
• C) 3.05
• D) 3.25

What should be the type of both variables in joint probability distribution of X and Y?

• A) One continuous and other discrete
• B) Both discrete
• C) Both continuous
• D) Either both continuous or both discrete

From the following table,
x 0 1 2 3
f (x) 0.26 0.49 0.22 0.02
F(x=2) will be:

• A) 0.97
• B) 0.49
• C) 0.99
• D) 0.23

The hypergeometric random variable is a(an):

• A) Undefined
• B) Independent
• C) Continuous variable
• D) Discrete variable

The two mutually exclusive outcomes in a Bernoulli trial are usually called:

• A) Variable and constant
• B) Mean and variance
• C) With and without replacement e trials are independent
• D) Success and failure

If f(x) = 1/10, x = 10, then E(X) is:

• A) 1
• B) 0
• C) -1
• D) 6/8

A correlation coefficient:

• A) is a sort of index of how close the points of a scattergram deviate from the best fitting straight line through those points.
• B) all of these.
• C) efficiently summarises some of the information in a scatterplot.
• D) tells you the direction of the slope of the scattergram.

Integrating the product of x and f(x) from range
–∞ to +∞ give us the

• A) Cumulative probability of x
• B) First moment about mean
• C) Total probability of x
• D) First moment about origin

Poisson distribution is the limiting form of binomial distribution when n, the number of trials is large and p, the probability of success is

• A) Moderately small
• B) very Small
• C) very Large
• D) Moderately large

In hyper geometric distribution; N = number of units in the population, n = number of units in the sample and k = number of successes in the population, then Variance of hyper geometric distribution is defined as:

• A) n.k/N ((N-k)/N)((N-n)/(N-k))
• B) n.k/N ((N-k)/n)((N-n)/(N-1))
• C) n.k/N ((N-1)/N)((N-n)/(N-1))
• D) n.k/N ((N-k)/N)((N-n)/(N-1))

Two discrete r.v.’s X and Y are said to be statistically independent, if and only if, for all possible pairs of values (Xi, Yj) the joint probability function f(x, y) can be expressed as the _______________ of the two marginal probability functions.

• A) Inverse
• B) Average
• C) Product
• D) Sum