HOMEWORK 3-16 - HOMEWORK 3 Winter 2016 Due date Monday...

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HOMEWORK 3 Winter 2016 Due date: Monday February 8 at 4 pm 1. A sequence of characters is transmitted over a channel that introduces errors with probability 0.01 p = . a) If N is the number of error-free characters until the first error, what is the pmf of N ? b) If we want to be 99% sure that at least 1000 characters are received correctly before a bad one occurs, what is the appropriate value of p ? 2. A data center has 10,000 disk drives. Suppose that disk drives fail at the rate of 10 per day. Furthermore, the time between failures is exponentially distributed. a) Find the probability that there are no failures in a given day. b) Find the probability that there are fewer than 10 failures in 2 days. c) Find the number of spare disk drives that should be available so that all failures in a day can be replaced with probability 99%. 3. Let X be a Gaussian random variable with mean m and variance 2 σ . Find ( ) 3 P X m σ < . 4. Let X be a geometric random variable with parameter
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