Suppose, for some c≥ 0, Y has probability density function fy(t) = cI(−1 ≤ t ≤ 1)+0.61(3 ≤t≤ 4).(a) Find the value of c.(b) Find Fy, the cumulative distribution function of Y.(c) Draw the graph of fy(t) for t € (−2, 5).(d) Draw the graph of Fy(t) for t € (-2,5).

Given that for some , Y has probability density function:

Answered: Suppose, for some c ≥ 0, Y has…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider a group of people who have received treatment for a disease such as cancer. Let t be the survival time, the number of years a person lives after receiving treatment. The density function giving the distribution of t is p(t) = Ce-Ct for some positive constant C, and the cumulative distribution function is P(t) = , p(x)dx. Think carefully about what the practical meaning of P(t) is, being sure that you can put it into words. a) The survival function, S(t), is the probability that a randomly selected person survives for at least t years. Find a formula for S(t). b) Suppose that a patient has a 80 percent chance of surviving at least 2 years. Find C. c) Using the value of C you found in (b), find the probability that the patient survives up to (that is, less than or equal to) 1 years. d) Using the value of C you found in (b), find the the mean survival time for patients with this survival function, in years.
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Suppose, for some c ≥ 0, Y has probability density function fy(t) = cI(−1 ≤ t ≤ 1)+0.61(3 ≤ t≤ 4). (a) Find the value of c. (b) Find Fy, the cumulative distribution function of Y. (c) Draw the graph of fy(t) for t € (−2,5). (d) Draw the graph of Fy(t) for t€ (-2,5).