Suppose that the continuous random variable X has a cumulative distribution function given by 0, if x < √2 x² -2 if √2 < x < √3 if √3 < x. 1, F(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). (d) Find the probability density function of X.
Suppose that the continuous random variable X has a cumulative distribution function given by 0, if x < √2 x² -2 if √2 < x < √3 if √3 < x. 1, F(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). (d) Find the probability density function of X.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 23E
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Question
![Suppose that the continuous random variable X has a cumulative distribution function given by
0,
if x < √2
if √√2<x< √3
if √3 ≤ x.
F(x) =
1,
-2
(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 ≤2/1).
(d) Find the probability density function of X.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7e7c908-505f-4c35-8ac4-e541f2ab69b2%2F82f8d71c-2a70-4b94-b5c0-7ef4814b7bc9%2Fc58ml4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that the continuous random variable X has a cumulative distribution function given by
0,
if x < √2
if √√2<x< √3
if √3 ≤ x.
F(x) =
1,
-2
(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 ≤2/1).
(d) Find the probability density function of X.
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