4 Iron ore is dug up to be crushed and filtered through a sieve prior to further processing. The sieve filters out any iron ore larger than 1cm in diameter. Let X be a random variable describing the diameter (in cm) of a piece that has made it through the sieve. Suppose that X has the beta distribution with parameters a = 4 and ß = 3. (a) Determine the cdf of X. (b) Calculate the mean and standard deviation of the diameter of iron ore pieces. (c) The dollar value V of an iron ore piece is proportional to its volume, specifically V = $ 5X³. Find E[V], the average dollar value of a piece that makes it through the sieve.
4 Iron ore is dug up to be crushed and filtered through a sieve prior to further processing. The sieve filters out any iron ore larger than 1cm in diameter. Let X be a random variable describing the diameter (in cm) of a piece that has made it through the sieve. Suppose that X has the beta distribution with parameters a = 4 and ß = 3. (a) Determine the cdf of X. (b) Calculate the mean and standard deviation of the diameter of iron ore pieces. (c) The dollar value V of an iron ore piece is proportional to its volume, specifically V = $ 5X³. Find E[V], the average dollar value of a piece that makes it through the sieve.
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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![4 Iron ore is dug up to be crushed and filtered through a sieve prior to further processing. The
sieve filters out any iron ore larger than 1cm in diameter. Let X be a random variable describing
the diameter (in cm) of a piece that has made it through the sieve. Suppose that X has the
beta distribution with parameters a = 4 and ß = 3.
(a) Determine the cdf of X.
(b) Calculate the mean and standard deviation of the diameter of iron ore pieces.
(c) The dollar value V of an iron ore piece is proportional to its volume, specifically V = $ 5X³.
Find E[V], the average dollar value of a piece that makes it through the sieve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feaf0af2a-3abd-4b05-8a4d-6ad3e8b11589%2Fdc8320b5-63f0-4b97-a2c1-a17fc2307fdf%2Fsjaz2ip_processed.png&w=3840&q=75)
Transcribed Image Text:4 Iron ore is dug up to be crushed and filtered through a sieve prior to further processing. The
sieve filters out any iron ore larger than 1cm in diameter. Let X be a random variable describing
the diameter (in cm) of a piece that has made it through the sieve. Suppose that X has the
beta distribution with parameters a = 4 and ß = 3.
(a) Determine the cdf of X.
(b) Calculate the mean and standard deviation of the diameter of iron ore pieces.
(c) The dollar value V of an iron ore piece is proportional to its volume, specifically V = $ 5X³.
Find E[V], the average dollar value of a piece that makes it through the sieve.
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