3. Let X be the number of traffic lights Amit encounters every day on his daily...

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3. Let X be the number of traffic lights Amit encounters every day on his daily commute. On average, he encounters 4.8 red lights on his daily commute, with a variance of 2.88. Find IP(X > 8) using (a) Markov's inequality, (b) Chebyshev's inequality, and (c) Chernoff's bound. In part (c), assume that px(x) = (2) (0.4)(1 - 0.4) 12-, i.e., X B(12,0.4). 2 3. Let X be the number of traffic lights Amit encounters every day on his daily commute. On average, he encounters 4.8 red lights on his daily commute, with a variance of 2.88. Find IP(X > 8) using (a) Markov's inequality, (b) Chebyshev's inequality, and (c) Chernoff's bound. In part (c), assume that px(x) = (2) (0.4)(1 - 0.4) 12-, i.e., X B(12,0.4). 2