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1. The radius R of a certain disk is a (a) What is the probability that 3 < R <4? continuous random variable with pdf fr(r) = 3r² 125' where 0

1. The radius R of a certain disk is a (a) What is the probability that 3 < R <4? continuous random variable with pdf fr(r) = 3r² 125' where 0

A First Course in Probability (10th Edition)
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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1. The radius \( R \) of a certain disk is a continuous random variable with pdf \( f_R(r) = \frac{3r^2}{125} \), where \( 0 < R < 5 \). \[ \begin{aligned} &\text{(a) What is the probability that } 3 < R < 4? \\ &\text{(b) Find and simplify a formula for the cdf } F_R(r) \text{ of the random variable } R. \\ &\text{(c) What is the expected value } E(R)? \\ \end{aligned} \] **Diagram:** The image includes a diagram of a circle with its center at the origin \((0,0)\) and radius \( R \). The point \((R, 0)\) is marked on the circumference. This diagram represents a disk whose radius is the variable \( R \).
Transcribed Image Text:1. The radius \( R \) of a certain disk is a continuous random variable with pdf \( f_R(r) = \frac{3r^2}{125} \), where \( 0 < R < 5 \). \[ \begin{aligned} &\text{(a) What is the probability that } 3 < R < 4? \\ &\text{(b) Find and simplify a formula for the cdf } F_R(r) \text{ of the random variable } R. \\ &\text{(c) What is the expected value } E(R)? \\ \end{aligned} \] **Diagram:** The image includes a diagram of a circle with its center at the origin \((0,0)\) and radius \( R \). The point \((R, 0)\) is marked on the circumference. This diagram represents a disk whose radius is the variable \( R \).
**Question (d):** What is the expected area of the disk of radius \( R \)? *(Think about this carefully!)* There are no graphs or diagrams associated with this text.
Transcribed Image Text:**Question (d):** What is the expected area of the disk of radius \( R \)? *(Think about this carefully!)* There are no graphs or diagrams associated with this text.
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