A random variable X has a cdf given by 0, x < 0 1x, 0 < x < 1 ¼x + ¼, 1 ) (c) Find P(X <3) (f) What is P(X= 2)? (g) Find E(3X²). (h) Find the 25th percentile of the distribution. Namely, find the value of 0.25 So that P(X ≤ 0.25) = F(0.25) = 0.25. (i) Find the conditional probability P(X > X >).

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A random variable X has a cdf given by
0,
x < 0
1x,
0 < x < 1
¼x + ¼, 1<x<3
x ≥ 3.
F(x) =
(a) Sketch the graph of F(x).
(b) Find the pdf f(x) of X, and sketch its graph.
(c) Find P(≤X ≤ 2).
^^
(d) Find P(X> )
(c) Find P(X <3)
(f) What is P(X= 2)?
(g) Find E(3X²).
(h) Find the 25th percentile of the distribution. Namely, find the value of 0.25 So
that P(X ≤ 0.25) = F(0.25) = 0.25.
(i) Find the conditional probability P(X > X >).
Transcribed Image Text:A random variable X has a cdf given by 0, x < 0 1x, 0 < x < 1 ¼x + ¼, 1<x<3 x ≥ 3. F(x) = (a) Sketch the graph of F(x). (b) Find the pdf f(x) of X, and sketch its graph. (c) Find P(≤X ≤ 2). ^^ (d) Find P(X> ) (c) Find P(X <3) (f) What is P(X= 2)? (g) Find E(3X²). (h) Find the 25th percentile of the distribution. Namely, find the value of 0.25 So that P(X ≤ 0.25) = F(0.25) = 0.25. (i) Find the conditional probability P(X > X >).
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