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

• A) number of successes in sample
• B) number of failures in the sample
• C) number of successes in population
• D) number of failures in population

When X and Y are ____________ variables, then their joint probability function can be obtained by multiplying together their marginal probability functions.

• A) Normal
• B) Dependent
• C) Bivariate
• D) Independent

$$According{\text{ }}to{\text{ }}emperical{\text{ }}rule,{\text{ }}how{\text{ }}much{\text{ }}data{\text{ }}lies{\text{ }}between\,\mu - \sigma \,and\,\mu + \sigma \,?$$

• A) 95.44%
• B) 75.66%
• C) 99.73%
• D) 68.26%

When the event occur randomly over a specified interval of time, space or length; the distribution is known as:

• A) Hyper geometric distribution
• B) Poisson Process.
• C) None of the above
• D) Poisson Distribution

If total probability of joint probability distribution f(x,y) is ONE then what will be the total probability of its marginal pdf g(x)?

• A) Half of the joint pdf
• B) Less than one
• C) Anywhere between zero and one
• D) One

The marginal p.d.f. of __________ variables is obtained by integrating the other variable from the joint p.d.f.

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

The marginal p.d.f. of any continuous variables is obtained by ___________ the other variable from the joint p.d.f.

• A) Dividing
• B) Multiplying
• C) Averaging
• D) Integrating

In binomial distribution, formula of calculating mean is:

• A) μ = qn
• B) μ = pq
• C) μ = np
• D) μ = p + q

Which of the following statements is true about the normal distribution?

• A) It has a U-shaped probability density function
• B) It is a discrete probability distribution
• C) It is completely determined by its mean and variance
• D) It is also known as the Poisson distribution

$${\text{In a normal distribution how much area lies between }}\mu \pm 3\sigma$$

• A) 70%
• B) 89%
• C) 68%
• D) 99.73%

If b(x, 7, 0.30), the variance of this distribution is:

• A) 1.77
• B) 1.47
• C) 1.74
• D) 1.44

The sum of the probabilities of bivariate probabilities function f(X, Y) is ONE then what will be the value of sum of its marginal probability function f(x)?

• A) Will be the average of two variables
• B) Depends on the Y variable
• C) Will be one
• D) May and may not be one

E(X + Y) = ?

• A) None
• B) E(X + Y) = E(X) E(Y).
• C) E(X + Y) = E(X) + E(Y).
• D) E(X + Y) = E(X) + E(Y).

When a coin is tossed 3 times, the probability of getting 3 or less tails is

• A) 0
• B) 1/2
• C) 1
• D) 3/5

Which property is true for the distribution function F(x)?

• A) F(x) is a non decreasing function
• B) F(x)is a non increasing function
• C) F(x) is a increasing function
• D) F(x) is a decreasing function

The second moment-ratio of a particular continuous probability distribution found to be is 3.845. What does this value tell us about the distribution?

• A) Flatter than normal distribution
• B) Normal distribution
• C) Neither very peaked nor flatter
• D) Higher peak than the normal distribution

If µ3 = 4.5 and µ2 = 3 then the skewness of the distribution will be:

• A) 1.5
• B) 2.7
• C) 0.75
• D) 3.25

When a coin is tossed 3 times, the probability of getting 3 tails is

• A) 3/8
• B) 2/8
• C) 1/2
• D) 1/8

Which statement is true for a discrete Uniform distribution?

• A) Its graphical shape of the data is like “U”.
• B) Cannot say anything without observing the actual data.
• C) Sometimes it becomes symmetrical.
• D) It is absolutely symmetrical distribution.

Which of the following statements is an example of a continuous random variable?

• A) The depth of Lake Michigan at a randomly chosen point on the surface
• B) All of the above
• C) The number of gas stations in Detroit
• D) The number of credit hours you have this semester