Question 8.2.1: Let X be a continuous random variable with mean µ = 10 and v......
Let X be a continuous random variable with mean µ = 10 and variance σ2 = 100/3. Using Chebyshev’s Inequality, find an upper bound for the following probabilities.
(a) P(|X − 10|≥ 2).
(b) P(|X − 10|≥ 5).
(c) P(|X − 10|≥ 9).
(d) P(|X − 10|≥ 20).
(a) 1
(b) 1
(c) 100/243
(d) 1/12
Related Answered Questions
Question: 8.2.5
Verified Answer:
(a) 1, 1/4, 1/9
(b) 1 vs. .3173, .25 vs. .0455, .1...
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: 8.2.11
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