(a) Find the smallest interval [a, b] such that of P(a ≤X ≤ b) = 1. (b) Find P(X = 1.6). (c) Find P(1 ≤ x ≤ 12/7).

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Suppose that the continuous random variable X has a cumulative distribution function given by
0,
R₁
1,
F(x) =
if x < √2
x² - 2 if √√2 < x <
if √3 < x.
(a) Find the smallest interval [a, b] such that of P(a ≤ X ≤ b) = 1.
(b) Find P(X = 1.6).
(c) Find P(1 < X < 1/12).
(d) Find the probability density function of X.
√3
Transcribed Image Text:Suppose that the continuous random variable X has a cumulative distribution function given by 0, R₁ 1, F(x) = if x < √2 x² - 2 if √√2 < x < if √3 < x. (a) Find the smallest interval [a, b] such that of P(a ≤ X ≤ b) = 1. (b) Find P(X = 1.6). (c) Find P(1 < X < 1/12). (d) Find the probability density function of X. √3
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