Question 1

A Poisson distribution with F1F1F1S1F1F1F10 = .60 is a:

Accepted Answer

A) symmetrical distribution. 
B) negatively skewed distribution (skewed to the left). 
C) positively skewed distribution (skewed to the right). 
D) binomial distribution. 
A) symmetrical distribution. 
B) negatively skewed distribution (skewed to the left). 
C) positively skewed distribution (skewed to the right). 
D) binomial distribution. C

Question 2

An analysis of the stock market produces the following information about the returns of two stocks: $\begin{array}{lcc} 
& \text { Stock } 1 & \text { Stock } 2 \
\hline \text { Expected Returns } & 15 \% & 18 \% \
\text { Standard Deviations } & 20 & 32 \
\hline  & &
\end{array}$ Assume that the returns are positively correlated, with F1F1F1S1F1F1F1012 = 0.80.
a. Find the mean and standard deviation of the return on a portfolio consisting of an equal investment in each of the two stocks.
b. Suppose that you wish to invest $1 million. Discuss whether you should invest your money in stock 1, stock 2, or a portfolio composed of an equal amount of investments on both stocks.

Accepted Answer

a. The expected return on the portfolio is E(0.5X1 + 0.5X2) = 0.5E(X1) + 0.5E(X2)= 16.5%.
The variance of the portfolio's return is (0.5 F1F1F1S1F1F1F10 20)2 + (0.5 F1F1F1S1F1F1F10 32)2 + 2(0.5)2 F1F1F1S1F1F1F10 0.80 F1F1F1S1F1F1F10 20 F1F1F1S1F1F1F10 32 = 612.
The standard deviation of the portfolio's return when F1F1F1S1F1F1F1012 = 0.80 is therefore 24.74%.
b. Your choice of investment in stock 1, the portfolio, or stock 2 depends on your desired level of risk (variance of return). The higher the risk you choose, the higher will be the expected return.

Question 3

State whether or not each of the following are valid probability distributions, and if not, explain why not. 
a. $\begin{array} { c | c c c c } 
x & 0 & 1 & 2 & 3 \
\hline p ( x ) & .15 & .25 & .35 & .45
\end{array}$
b. $\begin{array} { c | c c c c } 
x & 2 & 3 & 4 & 5 \
\hline p ( x ) & - .10 & .40 & .50 & .25
\end{array}$
c. $\begin{array} { c | c c c c c } 
x & - 2 & - 1 & 0 & 1 & 2 \
\hline p ( x ) & .10 & .20 & .40 & .20 & .10
\end{array}$

Accepted Answer

a. Not valid because the probabilities don't sum to one.
b. Not valid because it contains a negative probability.
c. Valid.

Question 4

The weighted average of the possible values that a random variable X can assume, where the weights are the probabilities of occurrence of those values, is referred to as the:

Accepted Answer

A) variance. 
B) standard deviation. 
C) expected value. 
D) covariance. 
A) variance. 
B) standard deviation. 
C) expected value. 
D) covariance.

Question 5

Phone calls arrive at the rate of 30 per hour at the reservation desk for a hotel.
a. Find the probability of receiving two calls in a five-minute interval of time.
b. Find the probability of receiving exactly eight calls in 15 minutes.
c. If no calls are currently being processed, what is the probability that the desk employee can take a four-minute break without being interrupted?

Accepted Answer

a. μ= 5(30/60) = 2.5; P(X = 2)

Question 6

A table, formula, or graph that shows all possible countable values a random variable can assume, together with their associated probabilities, is called a:

Accepted Answer

A) discrete probability distribution. 
B) continuous probability distribution. 
C) bivariate probability distribution. 
D) probability tree. 
A) discrete probability distribution. 
B) continuous probability distribution. 
C) bivariate probability distribution. 
D) probability tree.

Question 7

The Poisson random variable is a:

Accepted Answer

A) discrete random variable with infinitely many possible values. 
B) discrete random variable with a finite number of possible values. 
C) continuous random variable with infinitely many possible values. 
D) continuous random variable with a finite number of possible values. 
A) discrete random variable with infinitely many possible values. 
B) discrete random variable with a finite number of possible values. 
C) continuous random variable with infinitely many possible values. 
D) continuous random variable with a finite number of possible values.

Question 8

A bivariate distribution is a distribution is a joint probability distribution of two variables.

Accepted Answer

A) True 
 B)False

Question 9

Given that X is a binomial random variable, the binomial probability P(X $\geq$ x) is approximated by the area under a normal curve to the right of:

Accepted Answer

A) x - 0.5. 
B) x + 0.5. 
C) x - 1. 
D) x + 1. 
A) x - 0.5. 
B) x + 0.5. 
C) x - 1. 
D) x + 1.

Question 10

The probability distribution for X ,daily demand of a particular newspaper at a local newsagency,( in hundreds) is as follows: $$\begin{array} { l | r r r r } 
x & 1 & 2 & 3 & 4 \
\hline p ( x ) & 0.05 & 0.42 & 0.44 & 0.09
\end{array}$$ a. Find and interpret the expected value of X.
b. Find V(X).
c. Find F1F1F1S1F1F1F10.

Accepted Answer

a. E[X]=2.57 in hundreds of newspapers.

Question 11

Let X be a Poisson random variable with F1F1F1S1F1F1F10 = 6. Use the table of Poisson probabilities to find: 
a. $P ( X < 8 )$
b. $P ( X = 8 )$
c. $P ( X \geq 5 )$
d. $P ( 6 \leq X \leq 10 )$

Accepted Answer

a. 0.847.

Question 12

A recent survey in Victoria revealed that 60% of the vehicles travelling on highways, where speed limits are posted at 100 kilometres per hour, were exceeding the limit. Suppose you randomly record the speeds of 10 vehicles travelling on the Hume Highway, where the speed limit is 100 kilometres per hour. Let X denote the number of vehicles that were exceeding the limit. Find the following probabilities. 
a. P(X=10).
b. $P ( 4 < X < 9 )$
C. P(X=2).
d. $P ( 3 \leq X \leq 6 )$

Accepted Answer

X is a binomial rand

Question 13

The probability distribution for X is as follows: $$\begin{array} { l | r r r r } 
x & - 1 & 0 & 1 & 2 \
\hline p ( x ) & 0.1 & 0.25 & 0.55 & 0.1
\end{array}$$ Find the expected value of Y = X + 10.

Accepted Answer

The answer of The probability distribution for X is as...

Question 14

The number of people winning a lottery ticket each week is an example of a Poisson variable.

Accepted Answer

A) True 
 B)False

Question 15

The probability distribution for X is as follows: $$\begin{array} { l | r r r r } 
x & - 1 & 0 & 1 & 2 \
\hline p ( x ) & 0.1 & 0.25 & 0.55 & 0.1
\end{array}$$ a. Find E[5X + 1].
b. Find V[5X + 1].

Accepted Answer

The answer of The probability distribution for X is as...

Question 16

Given a binomial random variable with n =15 and p = 0.40, find the exact probabilities of the following events and their normal approximations.
a. X = 6.
b. X $\geq$ 9.
c. X $\leq$ 10.

Accepted Answer

a. Exact and approximated probabilities

Question 17

The P(X ≤ x) is an example of a cumulative probability.

Accepted Answer

A) True 
 B)False

Question 18

Which of the following best describes a discrete random variable?

Accepted Answer

A) A random variable that can only assume a countable number of values. 
B) A random variable that can only assume an uncountable number of values. 
C) All random variable are discrete random variables 
D) None of these choices are correct 
A) A random variable that can only assume a countable number of values. 
B) A random variable that can only assume an uncountable number of values. 
C) All random variable are discrete random variables 
D) None of these choices are correct

Question 19

Let X represent the number of computers in an Australian household, for those that own a computer. $$\begin{array} { | l | r | r | r | r | r | } 
\hline x & 1 & 2 & 3 & 4 & 5 \
\hline p ( x ) & 0.25 & 0.33 & 0.17 & 0.15 & 0.10 \
\hline
\end{array}$$ a. Find and interpret the expected number of computers in a randomly selected Australian household.
b. Find the variance of the number of computers in a randomly selected Australian household.

Accepted Answer

a. 2.52, computers. The long r

Question 20

The expected value, E(X), of a binomial probability distribution is:

Accepted Answer

A) n + p. 
B) np(1 - p). 
C) np. 
D) n + p - 1. 
A) n + p. 
B) np(1 - p). 
C) np. 
D) n + p - 1.

A Poisson distribution with  = .60 is a:

State whether or not each of the following are valid probability distributions, and if not, explain why not. a. x 0 1 2 3 p(x) .15 .25 .35 .45 b. x 2 3 4 5 p(x) -.10 .40 .50 .25 c. x -2 -1 0 1 2 p(x) .10 .20 .40 .20 .10

The weighted average of the possible values that a random variable X can assume, where the weights are the probabilities of occurrence of those values, is referred to as the:

A table, formula, or graph that shows all possible countable values a random variable can assume, together with their associated probabilities, is called a:

The Poisson random variable is a:

A bivariate distribution is a distribution is a joint probability distribution of two variables.

Given that X is a binomial random variable, the binomial probability P(X $\geq$ x) is approximated by the area under a normal curve to the right of:

The probability distribution for X ,daily demand of a particular newspaper at a local newsagency,( in hundreds) is as follows: x 1 2 3 4 p(x) 0.05 0.42 0.44 0.09 a. Find and interpret the expected value of X. b. Find V(X). c. Find .

Let X be a Poisson random variable with  = 6. Use the table of Poisson probabilities to find: a. $P ( X < 8 )$ b. $P ( X = 8 )$ c. $P ( X \geq 5 )$ d. $P ( 6 \leq X \leq 10 )$

The probability distribution for X is as follows: x -1 0 1 2 p(x) 0.1 0.25 0.55 0.1 Find the expected value of Y = X + 10.

The number of people winning a lottery ticket each week is an example of a Poisson variable.

The probability distribution for X is as follows: x -1 0 1 2 p(x) 0.1 0.25 0.55 0.1 a. Find E[5X + 1]. b. Find V[5X + 1].

Given a binomial random variable with n =15 and p = 0.40, find the exact probabilities of the following events and their normal approximations. a. X = 6. b. X $\geq$ 9. c. X $\leq$ 10.

The P(X ≤ x) is an example of a cumulative probability.

Which of the following best describes a discrete random variable?

The expected value, E(X), of a binomial probability distribution is:

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

Exam 7: Random Variables and Discrete Probability Distributions

A Poisson distribution with  = .60 is a:

State whether or not each of the following are valid probability distributions, and if not, explain why not. a. x 0 1 2 3 p(x) .15 .25 .35 .45 b. x 2 3 4 5 p(x) -.10 .40 .50 .25 c. x -2 -1 0 1 2 p(x) .10 .20 .40 .20 .10

The weighted average of the possible values that a random variable X can assume, where the weights are the probabilities of occurrence of those values, is referred to as the:

A table, formula, or graph that shows all possible countable values a random variable can assume, together with their associated probabilities, is called a:

The Poisson random variable is a:

A bivariate distribution is a distribution is a joint probability distribution of two variables.

Given that X is a binomial random variable, the binomial probability P(X ≥\geq≥ x) is approximated by the area under a normal curve to the right of:

The probability distribution for X ,daily demand of a particular newspaper at a local newsagency,( in hundreds) is as follows: x 1 2 3 4 p(x) 0.05 0.42 0.44 0.09 a. Find and interpret the expected value of X. b. Find V(X). c. Find .

Let X be a Poisson random variable with  = 6. Use the table of Poisson probabilities to find: a. P(X<8)P ( X < 8 )P(X<8) b. P(X=8)P ( X = 8 )P(X=8) c. P(X≥5)P ( X \geq 5 )P(X≥5) d. P(6≤X≤10)P ( 6 \leq X \leq 10 )P(6≤X≤10)

The probability distribution for X is as follows: x -1 0 1 2 p(x) 0.1 0.25 0.55 0.1 Find the expected value of Y = X + 10.

The number of people winning a lottery ticket each week is an example of a Poisson variable.

The probability distribution for X is as follows: x -1 0 1 2 p(x) 0.1 0.25 0.55 0.1 a. Find E[5X + 1]. b. Find V[5X + 1].

Given a binomial random variable with n =15 and p = 0.40, find the exact probabilities of the following events and their normal approximations. a. X = 6. b. X ≥\geq≥ 9. c. X ≤\leq≤ 10.

The P(X ≤ x) is an example of a cumulative probability.

Which of the following best describes a discrete random variable?

The expected value, E(X), of a binomial probability distribution is:

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

Given that X is a binomial random variable, the binomial probability P(X $\geq$ x) is approximated by the area under a normal curve to the right of:

Let X be a Poisson random variable with  = 6. Use the table of Poisson probabilities to find: a. $P ( X < 8 )$ b. $P ( X = 8 )$ c. $P ( X \geq 5 )$ d. $P ( 6 \leq X \leq 10 )$

Given a binomial random variable with n =15 and p = 0.40, find the exact probabilities of the following events and their normal approximations. a. X = 6. b. X $\geq$ 9. c. X $\leq$ 10.