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...

...variable X is a weighted average of the possible values that the random variable can take. Unlike the sample mean of a group 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)...

...QMT200
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...

...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...

...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...

...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...

...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....