In a probability mass function, the sum of all the probabilities is equal to:

• A) 2
• B) 1
• C) 3
• D) 0

When we draw the sample with replacement, the probability distribution to be used is:

• A) Hypergeometric
• B) Binomial
• C) Poisson
• D) Binomial & hypergeometric

Binomial distribution is skewed to the right if:

• A) p=n
• B) P<q
• C) p=q
• D) p>q

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

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

Poisson distribution can be used to approximate the hyper geometric distribution when; n <0.05N, n>20 and

• A) p<0.10
• B) p>0.10
• C) p<0.05
• D) p>0.05

What does it mean when a data set has a standard deviation equal to zero:

• A) The mean of the data is also zero
• B) Mean = median = mode
• C) All values of the data appear with the same frequency
• D) All of the values in the data are same

Most of the times Poisson approximation to the binomial is applied when p is less than 0.05 and n is greater than:

• A) 25
• B) 5
• C) 10
• D) 20

If X and Y are independent random variables, then Cov (X, Y) =

• A) 1
• B) 2
• C) 0
• D) 0.5

If b = 0, then E(ay+b) =

• A) y E(a)
• B) 0
• C) y E(a+b)
• D) a E(y)

Which of the following is NOT CORRECT about a standard normal distribution?

• A) P(Z = 2.0) = .0228
• B) P (Z = -2.5) = .4938
• C) P (Z = -1.0) = .03413
• D) P (0 = Z = 1.50) = .4332

The parameters of binomial distribution are:

• A) p,q
• B) n,p
• C) n,(n-1)
• D) n,p,q

In a discrete distribution function, F(23) can be stated as:

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

The probability of a continuous random variable X on any PARTICULAR point is always________:

• A) 0.5
• B) undefined
• C) 0
• D) 1

The number of typing errors per page in a book follows:

• A) Poisson Process
• B) Normal Distribution
• C) Hyper geometric Distribution
• D) Binomial Distribution

If c is a constant, then E(c) = _____

• A) c
• B) 1
• C) 0
• D) -c

The distribution function F(x) is equal to:

• A) All of the above
• B) P( X ≤ x)
• C) P(X = x)
• D) P( X ≥ x)

If E(x) = 3 then E(4X+3)=.....:

• A) 12
• B) 15
• C) 3
• D) 8

The mean of Hypergeometric distribution is:

• A) nk/N
• B) np
• C) npk
• D) npq

In statistics, the term ‘expected value’ implies the _____ value.

• A) Normal
• B) Independent
• C) Standard
• D) Mean

A random variable Y has the following distribution:
Y | -1 0 1 2
P(Y) | 3C 2C 0.4 0.1
Find the value of C?

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