. The radius R of a certain disk is a continuous random variable with pdf fR(r) = 3r 2 125, where 0 < R < 5. R (0, 0) (R, 0) (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)?
. The radius R of a certain disk is a continuous random variable with pdf fR(r) = 3r 2 125, where 0 < R < 5. R (0, 0) (R, 0) (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)?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 23E
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1. The radius R of a certain disk is a continuous random variable with
3r
2
125, where 0 < R < 5.
R
(0, 0) (R, 0)
(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)?
(d) What is the expected area of the disk of radius R? (Think about this carefully!)
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