# MA416 General prob-ability rules, conditional probability and Bayes theorem

Q1:5 Let Xi be Poisson distributed with parameter i for each i = 1; : : : ;m, and

suppose X1; : : : ;Xm are independent. Find the distribution of X1 + + Xm by the mgf.

(Hint: Compute the mgf of X1 + + Xm).

Q2：In a factory, there is a certain equipment which needs to be replaced immediately

after it goes bad. Let X1 and X2 denote the rst two times (in days) when the equipment

is replaced. The joint density of X1 and X2 is given by

fX1;X2(x1; x2) = e x2 ; 0 x1 x2:

(a) Compute the pdf of the lifetime of the equipment (i.e., the marginal pdf of X1).

(b) Suppose that the second replacement happened after 15 days. Given that, what is the

conditional distribution of the time of the rst replacement? (Hint: Find X1jX2 = 15.)

## Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)

# Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

### Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

### Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

### Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.