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Part 3 of 3 – Probability bounds
Question 1 of 2
0.0/ 12.0 Points
0.0/ 12.0 Points
Let Y1, Y2, …, Y9 are 9 i.i.d random variables, each with mean 9 and variance 4. Let M is the mean of these 9 random variables. i.e.,
M = (Yi + Y2 — Y9)/9
(a) Use the regular (two-sided) Chebyshev inequality to bound the probability that 111 is between 6 and 12. Your answer correct up to FOUR decimal places. No credit for rounding off.
(b) Use the regular (two-sided) Chebyshev inequality to bound the probability that M is between 6 and 12. Your answer correct up to FOUR decimal places. No credit for rounding off.
(c) Use the one-sided Chebyshev inequality (you may wish to use the expressions provided in the class notes) to bound the probability that M exceeds 12. Your answer 0.0270 correct up to FOUR decimal places. No credit for rounding off.
(d) Use the one-sided Chebyshev inequality (you may wish to use the two expressions provided in the class notes) to find the probability that M is between 6 and 12. Your answer correct up to FOUR decimal places. No credit for rounding off.