# 04spex2 - D denote the distance between them(a(20 points...

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Math 431 Second Evening Exam 6:15 - 7:15pm, April 13, 2004 M´arton Bal´azs NAME: 1. (35 points) A bakery puts chocolate chips in mufns. On average, how many chips should be put in one mufn iF the baker wants to have at least one chip in a mufn with probability 90%?

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2. (45 points) How many times should we fip a Fair coin iF we want at least 45%, at most 55% oF the outcomes to be heads with probability 99%? The standard normal distribution is to be found on the last page.
3. (35 points) Let X be a standard normal random variable. Compute the probability density function of Y = X 3 .

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4. We independently and randomly select two points on the same real interval (0 , 1). Let
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Unformatted text preview: D denote the distance between them. (a) (20 points) Find the probability distribution function of the random variable D . (b) (10 points) Find the probability density function of the random variable D . (c) (15 points) Find the expected value of D . Bonus question: (5 points) Now ±nd the expected value of D without the use of the distribution or density function, only by conditioning on the two points falling in the same half-interval, or one falling in (0 , 1 2 ) and the other in ( 1 2 , 1). In the ±rst case, the expectation is simply divided by two (why?), while in the second case it’s very easy to compute....
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04spex2 - D denote the distance between them(a(20 points...

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