Suppose the random variable T is the length of life of an object (possibly the lifetime of an electrical component or of a subject given a particular treatment). The hazard function hr(t) associated with the random variable T is defined by hr(t) = lims-o- P(t ≤T t) 8 Thus, we can interpret hr(t) as the rate of change of the probability that the object survives a little past time t, given that the object survives to time t. Show that if T is a continuous random variable, then hr(t) - fr(t) 1- Fr(t) = d dt log (1 - Fr(t)).

Suppose the random variable T is the length of life of an object (possibly the lifetime of an electrical component or of a subject given a particular treatment). The hazard function hr(t) associated with the random variable T is defined by hr(t) = lims-o- P(t ≤T t) 8 Thus, we can interpret hr(t) as the rate of change of the probability that the object survives a little past time t, given that the object survives to time t. Show that if T is a continuous random variable, then hr(t) - fr(t) 1- Fr(t) = d dt log (1 - Fr(t)).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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