i am in need of your help working on the following

1) Price Questions:

a) At what price are the laptops actually selling?

b) Does price change with time? (Hint: Make sure that the date column is recognized as such. JMP will then allow dynamic transformations and allow you to plot the data by weekly or monthly aggregates, or even by day of week. So create more "Date" columns in the graph builder by right clicking the date, and choosing "Date Time" so you can look at the Date with different aggregates such as Month, Day or Week, etc.)

c) Are prices consistent over retail outlets?

d) How do the sales volume in each store relate to Acell's revenues (based on prices)?

2) Location Questions:

a) Which stores are selling the most?

b) Where are the stores and customers located? Join the Customer and Store OS X and OS Y values Hint: This was in the in-class assignment so check the end of the posted walk-thru if you need help.

c) How far would customers travel to buy a laptop?

i) Hint 1: Use the coordinated highlighting between multiple visualizations in the same page, for example, select a store in one view to see the matching customers in another visualization.

ii) Hint 2: Explore the use of filters to see differences. Be sure to filter in the zoomed-out view. For example, try to use "store location" as an alternative way to dynamically compare store locations. This might be more useful to spot outlier patterns if there were 50 store locations to compare.

d) Try an alternative way of looking at how far customers traveled by creating a distribution graph showing this distance. A new column should be created that computes the distance between customer and store. (For information on creating formulas in JMP, search for "Creating Formulas" in the JMP documentation or see jmp.com/learn.). Use the Euclidean distance formula: where 1 is the customer location and 2 is the store location. For reference, my formula in JMP looks like this: To interpret this distance I looked at a few rows in the table and found the "crow flies" distance in miles between the zip codes and determined that an approximate calculation is Distance / 1604 to convert to miles. So the first row shows two zip codes that are approximately 1.5 miles apart (2405.9/1604) = 1.49.

3) Configuration Questions:

a) What are the details of each configuration? How does this relate to price? Hint: You will need to use a Table Join with the Laptops.txt file similar to how you joined in the post code data.

b) Do the stores sell all configurations?.

Q2. My home uses two light bulbs. On average, a light bulb last for 22 days (expo- nentially distributed). When a light bulb burns out, it takes and average of 2 days (exponentially distributed] before I replace the bulb. (a) Formulate a three-state birth and death process of this situation. (b Determine the fraction of the trne that both light bulbs are working. ) ((3) Determine the fraction of the time that no light bulbs are working. ) ((1 Suppose that Whenever a bulb burns out, a fixed failure cost of 5 dollars is incurred. Moreover, when any of the bulb is not working, an inconvenience cost of 1 dollar per bulb per day is incurred. Determine the long run cost per day for this system. PART 1: BIRTH AND DEATH RATES: For the select nations below, list both the current birth rate per 1000 people and the current death rate per thousand people. Then answer the questions below. (Look up the stats on the CIA World Factbook, under People. 1) CHINA 2) CANADA Birth Rate Birth Rate Death Rate Death Rate 3) NIGERIA 4) THAILAND Birth Rate Birth Rate Date Death Rate 5) FINLAND 6) PORTUGAL Birth Rate Birth Rate Death Rate Death Rate 7) UNITED ARAB EMIRATES 8) NEW ZEALAND Birth Rate Birth Rate Death Rate Death Rate 10) DEMOCRATIC REPUBLIC OF CONGO 9) ARGENTINA Birth Rate Birth Rate Death Rate Death RateA random walk is expressed as X] =Z, X, = X +Z, t=2.3..... where Z, - WN (Hz: 52 ). That is, E (Z, ) = /z: Var(Z, ) = o,, and Cov( Z,, Z; )=0 for t # s. Let {X,) be the random walk. (Z, ) is iid white noise with mean /, and variance o . And Z, is uncorrelated with X, . From the given information, X, is not stationary. So, mean and variance may vary with t. Thus, E [ X] ] = E [Z] ] = / E[X,] = E[X]] + E[Z,] and so on. = /4 + /2 That implies, E[X, ] = EM, The random walk is nonstationary in the mean when E [X] ] = E [X,] =... =[X,] =0 for all t. That is / =0, then the random walk is nonstationary in the mean. But in the I statement /2 0, so it is wrong. Therefore, statement I is false.For the simple symmetric random walk pengno,1,2... with $0 0, show that Pr$4 05 Pr$3 1s (i) with using the probability mass functions of 54 and $3 from class, (ii) without using the probability mass functions of $4 and $3 from class. Hint: In this case, use the fact that Pr93 is Pr93 is due to symmetrie of the symmetric random walk Exercise 5.1 For the simple symmetric random walk (S,)-0,1,2.... with So - 0, show that P[S - 0] - P[4 - 1] (i) with using the probability mass functions of S, and S; from class, (ii) without using the probability mass functions of S, and Sa from class. Hint: In this case, use the fact that PJS, = 1] = P[S, = -1] due to symmetric of the symmetric random walk (see also Problem 5.2)-Problem 7. A lazy random walk on an undirected graph is a Markov chain which evolves as follows. If the chain is at vertex v of the graph, a coin is flipped, whose heads is probability p. If the coin lands heads, then chain moves like the usual random walk (ie. it jumps to one of its neighbors, all equally likely). If the coin lands tails, the chain stays at v. Show that a lazy random walk on the n-cycle is ergodic and give its unique limiting distribution