Problem set Essay Example

Problem set Essay Problem set BY lu19920218 ECE 302 Problem Set 9 Fall 2013 The following problems have been selected from the course text. 4. 78 In a large collection of wires, the length of a wire is X, an exponential random variable with mean 511 cm. Each wire is cut to make rings of diameter 1 cm. Find the probability mass function for the number of complete rings produced by each length of wire. 4. 85 The exam grades in a certain class have a Gaussian pdf with mean m and standard deviation o. Find the constants a and b so that the random variable Y = ax + has a Gaussian pdf with mean m and standard deviation o . 4. 86, 4. 87 Let X = U n where n is a positive integer and U is a uniform random variable in the unit interval. Find the cdf and pdf of X. Repeat for the case where U is uniform in the interval [-1, 1]. 4. 94 modified Let Y = a where X is uniformly distributed in the interval (-1/2, 1/2). a. Show that Y is a Cauchy random variable. b. Find the pdf of Z = IN . 4. 96 Find the pdf of X† In(l U where U is a uniform random variable in (O, 1). . 9 modified Let X be a random variable with mean m. Compare the Chebyshev inequality and the exact probability for the event {IX m I c} as a function of c for the case where: a. X is a uniform random variable in the interval b]; b. X has pdf fX(x) = 2 exp(-alxl); c. X is a zero mean Gaussian random variable with variance 0 2 . 4. 100 Let X be the number of successes in n Bernoulli trials where the probability of success is p. Let Y = X/n be the average number of successes per trial. We will write a custom essay sample on Problem set specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Problem set specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Problem set specifically for you FOR ONLY $16.38 $13.9/page Hire Writer Apply the Chebyshev inequality o the event {IY pl a}. What happens as n †+ m? 4. 102 a. Find the characteristic function of the random variable X uniformly distributed over b). b. Find the mean and variance of X by applying the moment theorem. 4. 105 modified a. Show that the characteristic function of a Gaussian random variable X with mean m and variance 0 2 is 22 OX (w) = eJmw-o 12 . the characteristic function of Y = ax + b, a = O, where X is a Gaussian random variable. Hint: use the definition of (w), namely, OY (w) = E[eJwY ].

MBA Admissions Essay Sample

MBA Admissions Essay SampleIf you're on the lookout for an MBA admissions essay sample, you're in luck. We've gathered a few of the most popular and well known samples to help you when you're writing your own.'College Admissions Essay' by a Modern Parent: The authors discuss their history of raising children in this essay, including how they met their spouse. It's short, but it offers great insights into a parent's parenting style. Read it for inspiration!'You Could Be My Son or Daughter' by a Modern Parent: This essay is one that every parent should have a copy of. Not only does it contain a lot of useful tips, but it's also a lighthearted look at your children and why it's important to raise them as a single parent. An essential addition to any college admission essays collection. Recommended by both parents and teachers.'Thank You' From an MBA Admissions Student: It seems that almost everyone has written their own MBA admissions essay. This one focuses on why a student needs the a dmission letter in the first place. Why it was written? Why it was passed on?'Professionalism and Creativity' by an MBA Admissions Student: In this essay, you'll see just how important it is to use words that will entice and inspire. They will not only help to get your reader interested, but they will help the admissions committee to see what you're really about.'A Note About Writing,' by an MBA Admissions Student: The author shows just how much you can learn from studying admissions essays. Things you learn are things that you may find in this essay. While it is not something you'd want to use on its own, it can serve as an introduction to some of the best practices that you can use when writing your own.There are many more great MBA admissions essay samples out there. Which ones are your favorites? What is the one that you wish you could have read before you wrote yours?Getting ready to write your MBA admissions essay? Check out our guides and we'll tell you what it takes to ace t his big job. This article was written by Rachel Cavanagh and Felicia Robinson.