Question 8.2.3: Let X be the random variable of Exercise 2. (a) Calculate th......
Let X be the random variable of Exercise 2.
(a) Calculate the function f(x)= P(|X − 10|≥ x).
(b) Now graph the function f(x), and on the same axes, graph the Chebyshev function g(x) = 100/(3x2). Show that f(x) ≤ g(x) for all x> 0, but that g(x) is not a very good approximation for f(x).
f(x)\begin{cases} 1-x/10, & if 0 ≤ x ≤ 10; \\0 & otherwise\end{cases}
g(x)=\frac{100}{3x^2}.
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