We use the Poisson approximation to the binomial when:

• A) p is 0.04 or less & n is 15
• B) p is 0.01 or less & n is 10
• C) p is 0.02 or less & n is 10
• D) p is 0.05 or less & n is 50

For a binomial distribution, n= 10 & q= 0.6, the mean of the distribution is:

• A) 10
• B) 6.0
• C) 4
• D) 0.6

The joint density function f(x,y) will be a pdf if

• A) Both of integrals f(x,y) dx dy <1
• B) Both of integrals f(x,y) dx dy =0
• C) Both of integrals f(x,y) dx dy =1
• D) Both of integrals f(x,y) dx dy >1

if E(X + Y) = E(X) + E(Y) then E(X - Y)=

• A) E(X)E(Y)
• B) E(X)-E(Y)/E(X)
• C) E(X)- E(Y)
• D) E(X)/ E(Y)

Let X and Y be two random variables then the
Cov (X, Y) =

• A) E [Y – E(Y)]}
• B) 0
• C) E {[X – E(X)]
• D) E {[X – E(X)] [Y – E(Y)]}

Which of the following is not true statement for the hypergeometric distribution?

• A) Only two possible outcomes
• B) A constant probability of success
• C) A fixed number of trials
• D) Trials are dependent

Which of the following is correct property for joint probability distribution of X and Y:

• A) Both of the above
• B) None of the above
• C) $$\sum {f(Y,X)} = 1$$
• D) $$\sum {f(X,Y)} = 1$$

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

• A) 2
• B) 2.98
• C) 0.99
• D) 1.98

Position of the normal curve changes along the horizontal axis due to:

• A) Median
• B) Mode
• C) Standard deviation
• D) Mean

Which of the following is major property of hypergeometric distribution other than binomial distribution.

• A) It follows a continuous distribution
• B) The outcome of each trial may be classified into one of two categories
• C) The experiment is repeated a fix number of time
• D) The successive trials are not independent

The values of moment ratios b1 and b2 of normal distribution are:

• A) 0 and 2
• B) 0 and 3
• C) 0 and 4
• D) 0 and 1

The mean of the continuous probability function f(x) can be obtained by

• A) Integrating the product xf(x)
• B) Multiplying the x by its function f(x)
• C) Integrating the function f(x)
• D) Integrating the x

How many outcomes are there in a binomial experiment?

• A) It varies
• B) 2
• C) 1
• D) 0

Which of the probability distributions has three parameters?

• A) Poisson distribution
• B) Binomial distribution
• C) Normal distribution
• D) Hypergeometric distribution

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

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

If the first moment ratio is equal to 0, then the distribution will be:

• A) Leptokurtic
• B) Positively Skewed
• C) Negatively Skewed
• D) Symmetrical

The number of trials in hypergeometric distribution is:

• A) Fixed
• B) Not fixed
• C) Large
• D) Small

Poisson distribution is never:

• A) Positively Skewed
• B) Asymmetrical
• C) Symmetrical
• D) Negatively skewed

Which of the following is a characteristic of a binomial probability experiment?

• A) Probability of success changes for each trail
• B) Each trial has more than two possible outcomes
• C) P(success) = P(failure)
• D) The result of one trial does not affect the probability of success on any other trial

A random variable X has the probability distribution as follows:
X: 0 1 2 3
P(X): 2k 3k 13k 2k

What is the possible value of k?

• A) 0.01
• B) 0.07
• C) 0.05
• D) 0.03