homework07

homework07 - hours? 3. (2 pts) Let X be a uniform random...

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Probability for Engineering Applications Assignment #7, due at the beginning of class on Thursday, March 9 th , 2006 1. (2 pts) (Textbook exercise 3.45) A communication channel accepts an arbitrary voltage input v and outputs a voltage Y = v + N , where N is a Gaussian random variable with mean m = 0 and variance σ 2 = 1. Suppose the channel is used to transmit binary information as follows: to transmit 0 input -1 (i.e v=-1) to transmit 1 input +1 (i.e v=+1) The receiver decides that a 0 was sent if the voltage is negative and a 1 otherwise. Find the probability of the receiver making an error if a. a 0 was sent. b. a 1 was sent. 2. (2 pts) The lifetime of a transistor is normally distributed with mean 200 hours and standard deviation 9 hours (The probability of a negative lifetime is negligible). a. What is the probability that a particular transistor will last for more than 220 hours? b. What is the probability that a transistor which lasts for 210 hours will last for 220
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Unformatted text preview: hours? 3. (2 pts) Let X be a uniform random variable in the range [0 , 1] (i.e. a = 0 and b = 1) and let Y = 2 X + 3. Find the cdf, F Y ( y ) of Y . 4. (2 pts) (Textbook exercise 3.56) Suppose that a voltage X is a zero mean Gaussian random variable. Find the pdf of the power dissipated by a R ohm resistor P = RX 2 . 5. (2 pts) (Textbook exercise 3.57) A limiter Y = g ( X ) is shown in Figure 1 (on page 2). a. Find the cdf and pdf of Y in terms of the cdf and pdf of X . b. Find the cdf and pdf of Y if X is a Gaussian random variable with mean m and standard deviation . c. Find the cdf and pdf of Y if the input X = b sin U where U is uniformly distributed in the interval [0 , 2 ]. 1-a a x g(x) a-a Figure 1: Amplitude limiter 2...
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homework07 - hours? 3. (2 pts) Let X be a uniform random...

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