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1. The radius R of a certain disk is a continuous random variable with pdf fr(r) = 3r² 125' (a) What is the probability that 3 < R < 4? (b) Find and simplify a formula for the cdf Fr(r) of the random variable R. (c) What is the expected value E(R)? (0,0) where 0 < R < 5. R (R, 0)

1. The radius R of a certain disk is a continuous random variable with pdf fr(r) = 3r² 125' (a) What is the probability that 3 < R < 4? (b) Find and simplify a formula for the cdf Fr(r) of the random variable R. (c) What is the expected value E(R)? (0,0) where 0 < R < 5. R (R, 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 \( 0 < R < 5 \). (a) What is the probability that \( 3 < R < 4 \)? There is a diagram of a circle with center at the origin (0,0) and radius \( R \). The point on the circumference at (R,0) is marked. (b) Find and simplify a formula for the cdf \( F_R(r) \) of the random variable \( R \). (c) What is the expected value \( E(R) \)?
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 \( 0 < R < 5 \). (a) What is the probability that \( 3 < R < 4 \)? There is a diagram of a circle with center at the origin (0,0) and radius \( R \). The point on the circumference at (R,0) is marked. (b) Find and simplify a formula for the cdf \( F_R(r) \) of the random variable \( R \). (c) What is the expected value \( E(R) \)?
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Please can you solve part d also. Thank you! 

(d) What is the expected area of the disk of radius R? (Think about this carefully!)
Transcribed Image Text:(d) What is the expected area of the disk of radius R? (Think about this carefully!)
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