An experiment consists of rolling 1 red die, 1 white die, and 1 blue die and noting the result of each roll. The dice are fair, and all out comes are equally likely,

What is the probability that the SUM of the results on the three dice is 7?

What is the probability that the sum is an odd number?

Please explain in detail.  

The random variable X, which denotes the interval between two consecutive events, has the PDF: fx (?) = 4?^( 2)?^( −2?) ? ≥ 0 If we assume that intervals between events are independent, determine the following: (a) The expected value of X. (b) The expected value of the interval between the 11th and 13th events (c) The probability that ? ≤ 6.

1. CPK and SGOT tests are used in the diagnosis of myocardial infarction (MI). When the CPK test is given to a patient who does not have a MI, the probability of a negative finding (i.e. its specificity) is 0.6. The probability that the SGOT test will be negative for a non-MI patient is 0.7. When both tests are given to a non-MI patient the probability that at least one is negative is 0.9. For a non-MI patient who has both tests:

1. What is the probability that both tests are negative?
2. What is the probability that both tests are positive?

Hints: (1) Answer is not 0.12 -- tests are not to be assumed to be independent.

           (2) Using 2-by-2 table to structure your calculations can help.

3. What is the probability that at least one test is positive?

The accompanying data set provides the closing prices for four stocks and the stock exchange over 12 days:

Using Excel's Data Analysis Exponential Smoothing tool, forecast each of the stock prices using simple exponential smoothing with a smoothing constant of 0.3.

For example, help me to understand how to complete the exponential smoothing forecast model for Stock A.

Date Forecast A

9/3/2010 ____

9/7/2010 ____

9/8/2010 ____

9/9/2010 ____

9/10/2010 ____

9/13/2010 ____

9/14/2010 ____

9/15/2010 ____

9/16/2010 ____

9/17/2010 ____

9/20/2010 ____

9/21/2010 ____

In a political science class there are 15 political science majors and 9 non-political science majors. 4 students are randomly selected to present a topic. What is the probability that at least 2 of the 4 students selected are political science majors? Express your answer as a fraction or a decimal number rounded to four decimal places.

if two people are randomly selected from a class of 30 students, what is the probability that they have the same birthday?

Give the expected value, variance, and probability distribution for the sum of a fair coin and a random real number chosen uniformly in the range [ -1, 1]. Sketch the PMF.

Problem 4: Suppose M is a random matrix, and x is a deterministic (fixed) column vector. Show that E[x' M x] = x' E[M] x, where x' denotes the transpose of x.

In the binomial function, negative binomial function, poisson distribution, I dont know what to do when we need to find a variable X. For example, If X is exactly at 0, 1 , 2, etc. Then I know that we only need to apply the formula and calculate it. However, in some cases like X <= 2, X >= 5, X > 4, etc, then I do not know how to calculate that X and how to apply the formula. Ex: If P( X >= 4) = 1 - P(X <= 3) and for X <= 3, we will calculate the sum of X = 0, X = 1, X = 2, X = 3. How to define when to use 1 - P(X <= 3) or how P(X = 4) = P(X <= 4) - P(X <= 3). It really hard for me to understand this concept. Is there any formula or any way to define it so you know when to subtract, or when to add it together? Thank you.

While the housing market was in recession and was not likely to emerge anytime soon, real estate investment in college towns continued to promise good returns (The Wall Street Journal, September 24, 2010). Michele Gibellino worked for an investment firm in Michigan. Her assignment was to analyze the rental market in Ann Arbor, which is home to the University of Michigan. She gathered data on monthly rent for 2011 for a sample of 40 homes. The data is shown in the accompanying table.

Monthly Rent Monthly Rent Monthly Rent Monthly Rent

645 905 1084 1518

675 929 1100 1600

760 960 1100 1635

800 975 1185 1635

820 990 1245 1650

850 995 1275 1750

855 1029 1275 1950

859 1039 1400 1975

900 1049 1450 2200

905 1050 1500 2400

Tell me about the monthly rents. Choose the appropriate description.

Please show all work and all steps.

1.) Two cards are drawn from a standard 52-card playing deck. What is the probability that the draw will yield an ace and a face card?

2.) Articles coming through an inspection line are visually inspected by two successive inspectors. When a defective article comes through the inspection line, the probability that it gets by the first inspector is .1. The second inspector will "miss" five out of ten of the defective items that get past the first inspector. What is the probability that a defective item gets by both inspectors?

3.) A diagnostic test for a disease is such that it (correctly) detects the disease in 90% of the individuals who actually have the disease. Also, if a person does not have the disease, the test will report that he or she does not have it with probability .9. Only 1% of the population has the disease in question. If a person is chosen at random from the population and the diagnostic test indicates that she has the disease, what is the conditional probability that she does, in fact, have the disease? Are you surprised by the answer? Would you call this diagnostic test reliable?

QUESTION 1

1. Which of the following statements is TRUE?

   	a.	The average amount of safety stock depends on the size of orders placed with the supplier.
   	b.	The average amount of safety stock depends on the frequency in which orders are placed with the supplier.
   	c.	Cycle stock is the amount of inventory on hand when an order from the supplier is placed.
   	d.	Safety stock is the expected amount of inventory on hand when an order arrives from the supplier.
   	e.	All four answer choices are TRUE

1 points   

QUESTION 2

1. Consider an oilfield service company ( OSC ) that stocks a specific type of compressor, which they source from an American supplier. Since this compressor is the only product that OSC sources from that specific supplier, and given relatively steady demand of 2,000 compressors throughout the year, OSC uses a Continuous Review (Q) system for managing the inventory of this compressor. Orders to replenish stock requires administrative and other work that is estimated to be $40 per order. The compressors are purchased from the supplier for $325 each. It is estimated that annual inventory holding costs are 27% of the value of the item. The time from when an order is placed with the supplier until it arrives averages three weeks (including time to clear customs).

   What is the order quantity that OSC should use for these compressors if they wish to minimize total annual holding and ordering costs?

   	a.	115
   	b.	44
   	c.	22
   	d.	52
   	e.	43

1 points   

QUESTION 3

1. The Cheezy-Pretz corporation manufactures and distributes cheese-coated pretzels. They purchase their cheese, which come from a specific supplier in 10 kg packages, in batches of 500 kg (i.e. they currently order in lots of 50 packages at a time). This amounts to approximately an order every month, since annual demand is 600 packages. Each package costs Cheezy-Pretz $7, and they estimate that holding a package in inventory costs $1.75 per year. Further, they have studied their ordering process and estimate that it costs them $35 to place an order. They have been told that if they find the optimal order quantity, they could save money on annual ordering plus holding costs. Cheezy-Pretz would like to know how much they would save per year in ordering plus holding costs if they used the EOQ rather than their current order quantity of 50 packages at a time.

   	a.	<$100 per year
   	b.	>100 per year but < $150 per year
   	c.	>$150 per year but < $200 per year
   	d.	>$200 per year but < $250 per year
   	e.	>$300 per year

QUESTION 4

1. A night club that operates seven days a week uses a periodic review system where they check the stock of beer and liquor every Tuesday (at noon) and place an order that arrives on Thursday (at noon). They have found that demand for Silk beer ( smooth as silk ) averages 4.5 units per day with a standard deviation of 1.75 units. In any given week, they would like to be 95% sure that they don’ t run out of Silk beer before their order arrives. On Tuesday, if they have 16 units of beer on hand, how many units should they order?

   	a.	38
   	b.	39
   	c.	34
   	d.	23
   	e.	43

1 points   

QUESTION 5

1. The QRS Restaurant Supplier Co. is a wholesaler/distributor that supplies clients in the restaurant business with fresh perishables (e.g., produce) as well as equipment and supplies. One product that QRS provides to their customers (restaurants) is plastic stretch-wrap that comes in special extra-large rolls. QRS sells rolls from their inventory to their customers, and the inventory at the QRS warehouse is replenished by the stretch-wrap manufacturer in Ann Arbor, MI.

   QRS collected the following specific inventory-related data :
   
   Weekly demand (in rolls): average 42/week; standard deviation 16/week
   
   Annual demand (in rolls; assuming that demand occurs 52 weeks/year): 2,184
   
   Purchase price (QRS pays manufacturer) per roll: $54 Canadian
   
   QRS cost to place order with manufacturer: $35 per order (includes administrative costs to issue purchase order, invoice payment, etc.)
   
   XYZ annual cost to hold inventory: 23% of value
   
   Lead time for replenishment from manufacturer: three weeks
   
   Your Question: QRS currently places a replenishment order for rolls when their inventory position reaches 160 units. What cycle-service level does this imply?

   	a.	98.9%
   	b.	73.9%
   	c.	89.0%
   	d.	96.4%
   	e.	92.9%

QUESTION 6

1. Which of the following statements is TRUE?:

   	a.	A Periodic Review system requires less safety stock than a Continuous Review system.
   	b.	Over the long run, a Periodic Review (P) system and a Continuous Review (Q) system will generally have the same average order frequency and order size as each other (assuming that the manager aims to minimize the total of annual holding and ordering costs in both of the cases).
   	c.	In a Periodic Review system, order quantities tend to remain the same from order to order, while in a Continuous Review system, order quantities tend to vary from order to order.
   	d.	A Periodic Review system requires a computerized record-keeping system to maintain constant awareness of inventory position.
   	e.	All four answer choices are TRUE

QUESTION 7

1. A gas processing plant has a vat of important industrial lubricant for the machinery at the plant. Since an external supplier is responsible for maintaining the inventory of the lubricant, the supplier has a sensor set up on the vat that sends them a notification (by text message) as soon as the vat reaches a specific level of remaining volume. The demand for the lubricant averages 19 litres per day (with a standard deviation of 4.5), and the supplier requires a four-day lead time to refill the vat (assume it is exactly four days with no variability). If the supplier wishes to promise a 97.5% cycle-service level, at what volume should the sensor be set to contact the supplier? (Please double-check your answer, even if it shows up as one of the choices below.)

   	a.	76
   	b.	112
   	c.	94
   	d.	85

Patient satisfaction. Scores derived from a patient satisfaction survey are Normally distributed with μ = 50 and σ = 7.5, with high scores indicating high satisfaction. An SRS of n= 36 is taken from this population. What is the standard error (SE) of x for these data? We seek to discover if a particular group of patients comes from this population in which μ = 50. Sketch the curve that describes the sampling distribution of the sample mean under the null hypothesis. Mark the horizontal axis with values that are ±1, ±2, and ±3 standard errors above and below the mean. Suppose in a sample of n= 36 from this particular group of patients the mean value of x is 48.8. Mark this finding on the horizontal axis of your sketch. Then compute a z statistic for this scenario and make sure it matches your sketch. What is the two-sided alternative hypothesis for this scenario? Find the corresponding p-value for your z-statistic using Table B. Draw a conclusion for this study scenario based on your results

The number of products sold for the past several months is given along with the forecasts using both 3-month moving average and exponential smoothing (α = .2). Determine the better forecast using the MSE.

The Easy Credit Company report the following table representing a breakdown of customers accounting to the amount they owe and whether a cash advance has been made. An auditor randomly selects one of the accounts.

Show your work!

1. What is the probability that a customer received a cash advance?
2. What is the probability that a customer owed less than $200 and received a cash advance?
3. What is the probability that a customer owed less than $200 or received a cash advance?
4. Given that the customer-owned $1000 or more, what is the probability that the customer received a cash advance?
5. Are the events "receiving a cash advance" and "owning $1000 or more" independent? Explain why or why not.