A scientist always starts their experiment exactly at the scheduled time and finishes it at some random time between 1 and 3 hours later. Let X be the time (in hours) that elapses between the start of the experiment and its conclusion, and suppose the probability density function (pdf) f(x) = {kx(3 – - x), 0, 1 ≤ x ≤ 3 otherwise (a) (5 pts) Find the value of k. (Hints: f(x) dx = 1.) (b) (5 pts) Find the cumulative distribution function F(x). (c) (5 pts) What is the probability that the experiment will continue for between 2.5 and 3 hours? (d) (5 pts) What is the probability that the experiment lasts for at least 2.8 hours?
A scientist always starts their experiment exactly at the scheduled time and finishes it at some random time between 1 and 3 hours later. Let X be the time (in hours) that elapses between the start of the experiment and its conclusion, and suppose the probability density function (pdf) f(x) = {kx(3 – - x), 0, 1 ≤ x ≤ 3 otherwise (a) (5 pts) Find the value of k. (Hints: f(x) dx = 1.) (b) (5 pts) Find the cumulative distribution function F(x). (c) (5 pts) What is the probability that the experiment will continue for between 2.5 and 3 hours? (d) (5 pts) What is the probability that the experiment lasts for at least 2.8 hours?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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Transcribed Image Text:A scientist always starts their experiment exactly at the scheduled time and finishes it at
some random time between 1 and 3 hours later. Let X be the time (in hours) that elapses
between the start of the experiment and its conclusion, and suppose the probability density
function (pdf)
f(x) = {kx(3 –
- x),
0,
1 ≤ x ≤ 3
otherwise
(a) (5 pts) Find the value of k. (Hints: f(x) dx = 1.)
(b) (5 pts) Find the cumulative distribution function F(x).
(c) (5 pts) What is the probability that the experiment will continue for between 2.5
and 3 hours?
(d) (5 pts) What is the probability that the experiment lasts for at least 2.8 hours?
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