14. If x has the probability distribution f(x) = 12x for x = 1,2,3,…, show that E(2X) does not exist. This is famous Petersburg paradox, according to which a player’s expectation is infinite (does not exist) if he is to receive 2x dollars when, in a series of flips of a balanced coin, the first head appears on the xth flip. 17. The manager of a bakery knows that the number of chocolate cakes he can sell on any given day is a random variable having the probability distribution f(x) = 16 for x = 0,1,2,3,4, and 5. He also knows that there is a profit of $ 1.00 for each cake which he sells and a loss (due to spoilage) of $0.40 for each cake he does not sell. Assuming that each cake can be sold only on the day it is made, find the baker’s expected profit for a day on which he bakes

a. 3 of the cakes;
b.4 of the cakes;
c.5 of the cakes.
18. If a contractor’s profit on a construction job can be looked upon as a continuous random variable having the probability density For -1 < x < 5
elsewhere
(x+1)

f(x) = { 118 0

22. Mr. Adams and Ms. Smith are betting on repeated flips of a coin. At the start of the game Mr. Adams has a dollars, Ms. Smith has b dollars, at each flip the loser pays the winner one dollar, and the game continues until either player is “ruined.” Making use of the fact that in an equitable game each player’s mathematical expectation is zero, find the probability that Mr. Adams will win Ms. Smith’s b dollars before he loses his a dollars.

...PROBABILITY DISTRIBUTION
In the world of statistics, we are introduced to the concept of probability. On page 146 of our text, it defines probability as "a value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur" (Lind, 2012). When we think about how much this concept pops up within our daily lives, we might be shocked to find the results. Oftentimes, we do not think in these terms, but imagine what the probability of us getting behind the wheel of a car twice a day, Monday through Friday, and arriving at work and home safely. Thankfully, the probability for me has been 'one'! This means that up to this point I have made it to work and returned home every day without getting into an accident. While probability might have one outcome with one set of circumstances, this does not mean it will always turn out that way. Using the same example, just because I have arrived at work every day without getting into an accident, this does not mean it will always be true. As I confess with my words, and pray it does stay the same, probability tells me there is room for a different outcome.
In business, we often look at the probability of success or financial gain when making a decision. There are several things to take into consideration such as the experiment, potential outcomes, and possible events. An...

...of observations, which gives each observation equal weight, the mean of a random variable weights each outcome xi according to its probability, pi. The mean also of a random variable provides the long-run average of the variable, or the expected average outcome over many observations.The common symbol for the mean (also known as the expected value of X) is , formally defined by
Variance - The variance of a discrete random variable X measures the spread, or variability, of the distribution, and is defined by
The standard deviation is the square root of the variance.
Expectation - The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being weighted according to the probability of that event occurring. The expected value of X is usually written as E(X) or m.
E(X) = S x P(X = x)
So the expected value is the sum of: [(each of the possible outcomes) × (the probability of the outcome occurring)].In more concrete terms, the expectation is what you would expect the outcome of an experiment to be on average.
2. Define the following;
a) Binomial Distribution - is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. Therewith the probability of an event is defined by its binomial...

...CHAPTER 3: PROBABILITY DISTRIBUTION
3.1
RANDOM VARIABLES AND PROBABILITY DISTRIBUTION
Random variables is a quantity resulting from an experiment that, by chance, can assume different values. Examples of random variables are the number of defective light bulbs produced during the week and the heights of the students is a class. Two types of random variables are discrete random variables and continuous random variable.
3.2
DISCRETE RANDOM VARIABLE
A random variable is called a discrete random variable if its set of posibble outcomes is countable. Probability distribution is a listing of all the outcomes of an experiment and the probability associated with each outcome. For example, the probability distribution of rolling a die once is as below: Outcome, x Probability, P(x) 1 1 6 2 1 6 3 1 6 4 1 6 5 1 6 6 1 6
The probability distribution for P(x) for a discrete random variable must satisfy two properties: 1. The values for the probabilities must be from 0 to 1; 0 ≤ ( ) ≤ 1 2. The sum for P(x) must be equal to 1; ∑ ( ) = 1
QMT200
3.2.1 FINDING MEAN AND VARIANCE Mean of X is also referred to as its “expected value”.
= ( ) Where: = ∑[ ( )]
( )=
= (
) − [ ( )]
(
)=
[
( )] = ( )
Example 1 An experiment consists of tossing two coins simultaneously. Write down the sample space. If X is the number of tails observed,...

...equal to 6. If you add 10 to every score, the new mean will be 5 + 10 = 15; and the new median will be 6 + 10 = 16.
Suppose you multiply every value by a constant. Then, the mean and the median will also be multiplied by that constant. For example, assume that a set of scores has a mean of 5 and a median of 6. If you multiply each of these scores by 10, the new mean will be 5 * 10 = 50; and the new median will be 6 * 10 = 60.
Test Your Understanding of This Lesson
Problem 1
Four friends take an IQ test. Their scores are 96, 100, 106, 114. Which of the following statements is true?
I. The mean is 103.
II. The mean is 104.
III. The median is 100.
IV. The median is 106.
(A) I only
(B) II only
(C) III only
(D) IV only
(E) None is true
Solution
The correct answer is (B). The mean score is computed from the equation:
Mean score = Σx / n = (96 + 100 + 106 + 114) / 4 = 104
Since there are an even number of scores (4 scores), the median is the average of the two middle scores. Thus, the median is (100 + 106) / 2 = 103.
The Range
The range is the difference between the largest and smallest values in a set of values.
For example, consider the following numbers: 1, 3, 4, 5, 5, 6, 7, 11. For this set of numbers, the range would be 11 - 1 or 10.
The Interquartile Range (IQR)
The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles.
Quartiles divide a rank-ordered data set into four equal parts. The values that divide...

...PART A
Courts all over the world have set precedence’s of treating directors as trustees which means in the performance of their assigned legal and corporate duties, they stand in a fiduciary relation to the shareholders of the company. A director as a trustee shall act in the best of his ability to benefit the company and not in furtherance of his own interest.
Each of the four directors of the company stand in a fiduciary position to the company and thus liable for their acts of omission and commission to the shareholders of the company. They did not take adequate safeguards while deciding to invest a relatively huge sum of $20 million in a completely new business venture.
Section 232(2) and (3) of the Corporations Act has provided the followings:
An officer including a director of a corporation shall be duty bound to act with honesty of intentions as well as actions while exercising his powers vested while discharging his duties. This has been well documented in the case of Australian Growth ResourcesCorporation Pty Ltd v. Van Reesma (1988) 13 ACLR 261.Arthur who has already acquired stakes in Weaves Pty Limited should have disclosed his position to the Board of directors of Chance ltd. He was in a position to influence the Board and thus acted with sufficient and provable dishonesty. He is liable to be prosecuted under s.233.
It has been an established fact that if certain business decisions are taken and they don’t serve any rational purpose for the betterment...

...
NAME: SHU ZHAOHUI
ID: 17329164
Q5.
Descriptive Statistics |
| N | Minimum | Maximum | Mean | Std. Deviation | Skewness |
| Statistic | Statistic | Statistic | Statistic | Statistic | Statistic | Std. Error |
Gasolinescore | 1000 | 3.00 | 21.00 | 14.9090 | 4.83654 | -.493 | .077 |
Globalscore | 1000 | 3.00 | 21.00 | 17.0490 | 3.78774 | -1.073 | .077 |
Valid N (listwise) | 1000 | | | | | | |
The mean in the gaslinescore and globalscore stand for the average the respondents choose is 14.9090 and 17.0490, the respondents choose is concentrate around 14.9090 and 17.0490.
The standard deviation of gasolinescore refer to most of the respondents answer is rang from (14.9090-4.83654) to (14.9090+4.83654), and the standard deviation of globalscore refer to most of the respondents answer is rang from (17.0490-3.78774) to (17.0490+3.78774), and the globalscore’s float is smaller than gasolinescore’s float.
The data for Gasolinescore and Globalscore are not the normally distributed. Because the normally distributed situation means the median equal to mean. but in the table of above, the gaslinescore’s median(12) is not equal to the mean(14.9090) and the globalscore’s median(12) also not equal to mean(17.0490), they are all negative skew. So the data of each variable is not a normally distributed.
If the two variables were normally distributed, the median should be equal to mean, so the mean is 12, and the standard deviation is 4.83654 for gasolinescore; the standard...

...Proposing a Solution
I live outside of a small town of 3,000 people. The water system of our small town supplies drinking water to a population of 3,000 to 5,000. Our water system has been in place for 20 plus years and neglect has been rampant for almost the same period of time.
Public water systems are governed by regulations and monitored by the State of Louisiana. The Town of Ferriday has been under state mandated “boil orders” more times that you could count. One of the more recent events was when the State Inspectors arrived to conduct a regular inspection of the water treatment plant and found that a portion of the top of the water storage tank had collapsed and fallen in. The regulations state that potable water must be stored in such a way to prevent any contamination from outside sources. Inspectors found dead birds and debris in the town drinking water supply. National Guard supplied tankers that were placed all around town and filled with potable water from a nearby town. Our citizens were only able to get drinking water by bringing their own bottles or containers out and filling them at these tanker locations. This went on for months as a new water storage tank was constructed. The town had to bid the construction of the tank and argue about the companies’ bids, then finally award and construct the new tank.
During all of this, the finger pointing was rampant and everyone blames someone else or the prior administration in the...

...CHAPTER 10
CRITICISMS OF ABSORPTION COST SYSTEMS:
INCENTIVE TO OVER-PRODUCE
P 10-1: Solution to Federal Mixing (10 minutes)
[Explaining absorption versus variable costing]
Variable costing writes off to income all fixed manufacturing costs incurred during the year. Absorption costing prorates the fixed overheads between units in inventory and units sold based on machine hours.
Absorption costing net income is higher than under variable costing by $1.2 million. This means that inventories under absorption costing are higher by $1.2 million.
The ending work-in-process inventory contains 20,000 more machine hours than the beginning inventory (90,000 – 70,000 machine hours). From the data given, the fixed overhead rate applied to products is $60 per machine hour. Or,
$1.2 million = (90,000 – 70,000) × fixed overhead rate
Fixed overhead rate =
= $60
P 10–2: Solution to Xerox (15 minutes)
[Incentives to over produce]
By building inventories and using absorption costing, Xerox shifts some of its fixed manufacturing costs from cost of goods sold to inventories. This decreases cost of goods sold and increases net income as long as average unit costs are decreasing. This is a short-term strategy to boost accounting earnings and earnings will reverse as soon as inventories are depleted. This strategy is unlikely to mislead the stock market. Since the higher inventories must be disclosed as part of the...