I Failure rate for a uniformly distributed variable

AI Thread Summary
The discussion centers on determining the failure rate for a uniformly distributed random variable T over the interval [a, b]. The failure rate is defined as the ratio of the probability density function (pdf) to the complementary cumulative distribution function (cdf). Participants are asked to compute the pdf and cdf for a uniform distribution to apply this formula. The pdf for a uniform distribution is straightforward, leading to a discussion on how to derive the failure rate from these functions. Understanding the failure rate in this context is essential for applying the concept to uniform distributions.
Mark J.
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Hi,
I have this question:
If random variable T is uniformly distributed over [a, b] , what is its failure rate?
Please help
 
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What does failure rate mean here?
 
Office_Shredder said:
What does failure rate mean here?
The only instruction I got is failure rate for exponential distribution as image attached
 

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So the failure rate is f(t)/(1-F(t)) where f and F are the pdf and cdf of the distribution. Can you compute them for a uniform distribution? The pdf is fairly simple.
 

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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