Question 1

If X and Y are two independent random variables with V(X) = 6 and V(Y) = 5, then V(3X + 2Y) is: $$\begin{array} { | l | l | } 
\hline \text { A. } & 11 . \
\hline \text { B. } & 158 . \
\hline \text { C. } & 28 . \
\hline \text { D. } & 74 . \
\hline
\end{array}$$

Accepted Answer

The answer of If X and Y are two independent...

Question 2

An analysis of the stock market produces the following information about the returns of two stocks:   Assume that the returns are positively correlated, with   12 = 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

Question 3

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 $\sigma$.

Accepted Answer

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

Question 4

Let X be a binomial random variable with n = 25 and p = 0.01.
a. Use the binomial table to find P(X = 0), P(X = 1), and P(X = 2).
b. Approximate the three probabilities in part (a) using the appropriate Poisson distribution.
c. Compare your approximations in part (b) with the exact probabilities found in part (a). What is your conclusion?

Accepted Answer

a. P(X = 0) = 0.778, P(X = 1)

Question 5

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 6

The standard deviation of a binomial distribution for which n = 100 and p = .35 is:

Accepted Answer

A)   $4.77$. 
B)  $2.275$. 
C)  $47.7$. 
D)  $22.75$ 
A)   $4.77$. 
B)  $2.275$. 
C)  $47.7$. 
D)  $22.75$

Question 7

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

Accepted Answer

A) True 
 B)False

Question 8

A Bernoulli trial is where each trial of an experiment has four possible outcomes, the probability of success is p and the trials are not independent.

Accepted Answer

A) True 
 B)False

Question 9

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

b.
$\begin{array}{c|cccc}
x & 2 & 3 & 4 & 5 \
\hline p(x) & -.10 & .40 & .50 & .25
\end{array}$

c.
$\begin{array}{c|ccccc}
x & -2 & -1 & 0 & 1 & 2 \
\hline p(x) & .10 & .20 & .40 & .20 & .10
\end{array}$

Accepted Answer

a. Not valid because the proba

Question 10

The expected number of heads in 90 tosses of an unbiased coin is: $$\begin{array} { | l | l | } 
\hline \text { A. } & 30 . \
\hline \text { B. } & 45 . \
\hline \text { C. } & 50 . \
\hline \text { D. } & 60 . \
\hline
\end{array}$$

Accepted Answer

The answer of The expected number of heads in 90...

Question 11

For a discrete probability distribution to be valid, the probabilities must lie between 0 and 1, where the sum of all probabilities must be 1.

Accepted Answer

A) True 
 B)False

Question 12

The proprietor of a small hardware store employs three men and three women. He will select three employees at random to work on Christmas Eve. Let X represent the number of women selected.
a. Express the probability distribution of X in tabular form.
b. What is the probability that at least two women will work on Christmas Eve?

Accepted Answer

a. \[\begin{array} { c | c c c

Question 13

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 distributi on. 
D)  probability tree. 
A)  discrete probability distribution. 
B)  Continuous probability distribution. 
C)  bivariate probability distributi on. 
D)  probability tree.

Question 14

The joint probability distribution of X and Y is shown in the following table.  $\quad $ $\quad $ $\quad $ $\quad $$X$
$\begin{array}{c|ccc}
Y & 1 & 2 & 3 \
\hline 1 & .30 & .18 & .12 \
2 & .15 & .09 & .06 \
3 & .05 & .03 & .02
\end{array}$
 a. Determine the marginal probability distributions of X and Y.
b. Are X and Y independent? Explain.
c. Find P(Y = 2 | X = 1).
d. Find the probability distribution of the random variable X + Y.
e. Find E(XY).
f. Find COV(X, Y).

Accepted Answer

a. \[\begin{array} { c | c c c c c | c c

Question 15

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 $\le$ X $\le$ 6).

Accepted Answer

X is a binomial rand

If X and Y are two independent random variables with V(X) = 6 and V(Y) = 5, then V(3X + 2Y) is: A. 11. B. 158. C. 28. D. 74.

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 $\sigma$ .

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:

The standard deviation of a binomial distribution for which n = 100 and p = .35 is:

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

A Bernoulli trial is where each trial of an experiment has four possible outcomes, the probability of success is p and the trials are not independent.

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 expected number of heads in 90 tosses of an unbiased coin is: A. 30. B. 45. C. 50. D. 60.

For a discrete probability distribution to be valid, the probabilities must lie between 0 and 1, where the sum of all probabilities must be 1.

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

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Exam 7: Random Variables and Discrete Probability Distributions

If X and Y are two independent random variables with V(X) = 6 and V(Y) = 5, then V(3X + 2Y) is: A. 11. B. 158. C. 28. D. 74.

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 σ\sigmaσ .

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:

The standard deviation of a binomial distribution for which n = 100 and p = .35 is:

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

A Bernoulli trial is where each trial of an experiment has four possible outcomes, the probability of success is p and the trials are not independent.

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 expected number of heads in 90 tosses of an unbiased coin is: A. 30. B. 45. C. 50. D. 60.

For a discrete probability distribution to be valid, the probabilities must lie between 0 and 1, where the sum of all probabilities must be 1.

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

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

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 $\sigma$ .