Question 8.2.5: Let X be a continuous random variable with values normally d......
Let X be a continuous random variable with values normally distributed over (−∞,+∞) with mean µ = 0 and variance σ2 =1.
(a) Using Chebyshev’s Inequality, find upper bounds for the following probabilities: P(|X|≥ 1), P(|X|≥ 2), and P(|X|≥ 3).
(b) The area under the normal curve between −1 and 1 is .6827, between −2 and 2 is .9545, and between −3 and 3 it is .9973 (see the table in Appendix A). Compare your bounds in (a) with these exact values. How good is Chebyshev’s Inequality in this case?
Related Answered Questions
Question: 8.1.11
Verified Answer:
No, we cannot predict the proportion of heads that...
Question: 8.1.17
Verified Answer:
For x ∈ [0, 1], let us toss a biased coin that com...
Question: 8.1.15
Verified Answer:
Take as Ω the set of all sequences of 0’s and 1’s,...
Question: 8.2.1
Verified Answer:
(a) 1
(b) 1
(c) 100/243
(d) 1/12
Question: 8.2.11
Verified Answer:
(a) 0
(b) 7/12
Question: 8.2.13
Verified Answer:
(a) 2/3
(b) 2/3
(c) 2/3
Question: 8.2.17
Verified Answer:
E(X) =ʃ∞−∞ xp(x)dx. Since X is non-negative, we ha...
Question: 8.2.3
Verified Answer:
f(x)\begin{cases} 1-x/10, & if 0 ≤ x...
Question: 8.2.7
Verified Answer:
(b) 1, 1, 100/243, 1/12
Question: 8.2.9
Verified Answer:
(a) 0
(b) 7/12
(c) 11/12