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Unformatted text preview: nε 2 6. Does the weak law of large numbers hold for the sample mean if the X i ’s have the covariance functions given in Problem 1? Assume the X i have the same mean. 1 7. (a) A fair coin is tossed 100 times. Estimate the probability that the number of heads is between 40 and 60. Estimate the probability that the number is between 50 and 55. (b) Repeat part a for n = 1000 and the intervals [400 , 600] and [500 , 550]. 8. The number of messages arriving at a multiplexer is a Poisson random variable with mean 15 messages/second. Use the central limit theorem to estimate the probability that more than 950 message arrive in one minute. 9. A binary transmission channel introduces bit errors with probability 0.15. Estimate the probability that there are 20 or fewer errors in 100 bit transmissions. 2...
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- Winter '10
- Mean, Probability theory, one minute, 100 bit, covariance function COV