Math Is Fun Forum

soureddy.c

Member

Registered: 2007-11-11

Posts: 3

homework.....help needed......urgent

hi im unable to work on the following problem...........its my homewrk due within 1.5days......please do give me a solution....thanks a bunch.......

3)If the random variable T is the time to failure of a commercial product and the values of its probability density and distribution function at time "t" are   f(t) and F(t), then its failure rate at time t is given by f(t) / 1-F(t)
Thus, the failure rate at time t is the probability density of failure at time t given that failure does not occur prior to time t.
a)show that if t is an exponential distribution, the failure rate is constant.
b)show that if T has a weibull distribution thae failure rate is given by  (alpha *beta)*t^beta-1.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: homework.....help needed......urgent

(a) For the exponential distribution,

Substitute these into the failure-rate expression and simplify.

(b) I don’t know what the Weibull distribution is, so thank you Wikipedia!

Again substitute these into the the expression for the failure rate and simplify.