The total area under the normal curve is:

• A) 0
• B) 0.75
• C) 1
• D) 0.5

The binomial distribution is negatively skewed when:

• A) p=q
• B) p>q
• C) p=q=1/2
• D) p<q

If we have f(x) = 4x, 0≤x≤1, then f(x) is a:

• A) Probability density function
• B) Continuous random variable
• C) Distribution function
• D) Probability distribution

From joint distribution function f(X, Y), we can get marginal probabilities function, but vise versa is true when

• A) X and Y are dependent
• B) X and Y are highly correlated
• C) X and Y are independent
• D) X and Y are symmetrical

If the first moment ratio is less than 0, then the distribution will be:

• A) Negatively Skewed
• B) Symmetrical
• C) Nobe of these
• D) Positively Skewed

Let X and Y are TWO random variables. Which property of expectation is true?

• A) E(X + Y) = 2 E(X + Y)
• B) E(X + Y) = 2 * {E(X) + E(Y)}
• C) E(X + Y) = E(X) + E(Y) – E(XY)
• D) E(X + Y) = E(X) + E(Y)

Match the binomial probability P(x< 23) with the correct statement.

• A) P (there are more than 23 successes)
• B) P (there are at least 23 successes)
• C) P(there are at most 23 successes)
• D) P (there are fewer than 23 successes)

Which of the following is NOT applicable to a Poisson distribution?

• A) IF P = 0.02 & n = 300
• B) IF P = 0.01 & n = 200
• C) IF P = 0.5 & n = 19
• D) IF P = 0.03 & n = 500

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 0 (x=0) students waiting at the bus stop?

• A) 0.10
• B) 0.25
• C) 0.0
• D) 0.01

The function F(x) gives the probability of the event that X takes a value a value......

• A) P(X>x)
• B) P(X<x)
• C) P(X≤x)
• D) P(X=x)

Uniform distribution is a:

• A) Continuous Distribution
• B) Mixed
• C) None of the above
• D) Discrete distribution

An urn contains 4 red balls and 6 green balls. A sample of 4 balls is selected from the urn without replacement. It is the example of:

• A) Hypergrometric distribution
• B) Binomial distribution
• C) Poisson distribution
• D) Exponential distribution

x 0 1 2 3
f (x) 0.26 0.49 0.22 0.02
From the above table, the expected value will be equal to:

• A) 0.71
• B) 0.79
• C) 0.99
• D) 0.81

Conditional distribution of a random variable “X” is obtained by dividing joint distribution of “X” and “Y” by the

• A) Conditional distribution of “Y”.
• B) No0me of the above
• C) Marginal distribution of “X”.
• D) Marginal distribution of “Y”.

Two independent variables have bivariate distribution, then E(X.Y) =

• A) X.E(Y)
• B) Y.E(X)
• C) E(X).E(Y)
• D) X.Y

If p is very small and n is considerably large then we shall apply the:

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

The lottery conducted in various countries for purposes of money-making provides a good example of:

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

In a bivarite probability distribution of X and Y,
If E(X)=3 and E(Y)=5, then E(X-Y)= ?

• A) 15
• B) -2
• C) 2
• D) None of these

In a binomial experiment outcome can be classified into

• A) 3 Categories
• B) 1 Caategories
• C) None of the above
• D) 2 Categories

The second moment-ratio of a particular continuous probability distribution is 2.144. What does this value tell us about shape of the distribution?

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