Let X have the PDF f(x) = x3/c for some c>0 with space S = {x : 0 < x < 2}. If A1 = {x : 0 < x < 2/3} and A2 = {x : 1/3 < x < 1}, compute P(A1∩A2).

(a)5/432

(b)5/108

(c)5/27

(d)5/9

Let X have the PDF f(x) = x3/c for some c&gt;0 with space S = {x : 0 &lt; x &lt; 2}. If A1 = {x : 0 &lt; x &lt;2/3} and A2 = {x : 1/3 &lt; x &lt; 1}, compute P(A1∩A2).(a)5/432(b)5/108(c)5/27…

 

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Let X1, …,Xn be a random sample from a gamma distribution with parameter alpha and beta.a. Derive the equations whose solution yields the mle of alpha and beta . Do you think they can be solvedexplicitly?b. Show that the mle of μ = alpha x beta is ˆμ = ¯x.

 

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Let X1, X2 be two random variables with joint pdf f(x1, x2)=4x1x2, 0 < x1 < 1, 0 < x2 < 1, zero elsewhere. Compute E(X1), E(X21 ), E(X2), E(X22 ), and E(X1X2). Is E(X1X2) = E(X1)E(X2)? Find E(3X2 − 2X2 1 + 6X1X2).

Let X1, X2 be two random variables with joint pdf f(x1, x2) = 4x1x2, 0 &lt; x1 &lt; 1, 0 &lt; x2 &lt; 1,zero elsewhere.Compute E(X1), E(X21 ), E(X2), E(X22 ), and E(X1X2).Is E(X1X2) =…

 

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Letter Co. produces and sells two products, T and O. It manufactures these products in separate factories and markets them through different channels. They have no shared costs. This year, the company sold 50,000 units of each product. Sales and costs for each product follow.Product T Product O Sales $800,000 $800,000 Variable Costs 560,000 100,000 Contribution margin 240,000 700,000 Fixed Costs 100,000 560,000 Income before taxes 140,000 140,000 Income taxes (32% rate) 44,800 44,800 Net Income $95,200 $95,2001. Compute the break-even point in dollar sales for each product.2. Assume that the company expects sales of each product to decline to 33,000 units next year with no change in unit sales price. Prepare forecasted financial results for next year following the format of the contribution margin income statement as just shown with columns for each of the two products (assume a 32% tax rate). Also, assume that any loss before taxes yields a 32% tax savings.3. Assume that the company expects sales of each product to increase to 64,000 units next year with no change in unit sales price. Prepare forecasted financial results for next year following the format of the contribution margin income statement shown with columns for each of the two products (assume a 32% income tax rate).4. If sales greatly decrease, which product would experience a greater loss?5. Describe some factors that might have created the different cost structures for these two products.

SolutionGivenUnitsSale priceSalesVariable costContributionContribution per unitFixed costNet Income Product T Product O500005000016168000008000005600001000002400007000004.8…

 

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  The contact person for this position is: Terrence Walters, Hiring Manager, Hilton Corporation, 555 SW 8th St., Miami, FL 33199. Recommended Organization Introduction/Opening: Begin your letter with the bad news. The indirect approach includes a buffer, however, the direct approach does not. Be sure to remain professional and concise in this section to not sound rude or ungrateful for the opportunity. Body/Discussion: In the first paragraph of the body include your reasons for the decision, without too much detail about the other position. Having the right balance of ambiguity is respectful to the employer you are declining. Use creativity when developing reasons for taking the other position over theirs. Maybe the schedule was more flexible or the other position better fir your skill set. These are just a few examples to consider when writing this section.

In the second paragraph you can add a positive spin to the situation if you desire. This could be as simple as saying you’ll keep this employer in mind for future endeavors or that you will recommend a qualified friend who should apply for the position.

Conclusion/Closing: Begin your closing paragraph with a courteous transition and thank the employer for the opportunity. Conclude your letter by indicating how the reader may contact you if he has any questions.

In an effort to provide the best possible work force environment and toembrace diversity throughout our organization we have transitioned thetraditional Christmas Party to a Winter Celebration,…

 

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