Question

PHYS1047 a) Given a random variable x, with a continuous probability distribution function fx) 4 marks b) The life expectancy (in days) of a mechanical system has a probability density write down equations for the cumulative distribution C(x) and the survival distribution Px). State a relationship between them. function f(x)=1/x, for x21, and f(x)=0 for x <1. i Find the probability that the system lasts between 0 and I day.2 marks i) Find the probability that the system lasts between 0 and 10 days. 12 marks] ii) Find the probability that the system lasts more than 10 days.[2 marks iv) Find the cumulative distribution function Cx) of the system.[2 marko c) The memory-less property, for Vt,h>O, is defined by P(x2t+hlx2t) Px2h) From this show that 1-C(t+h) 2 marks) 2 marks 4 marks] ii) If L(x)-In[1-C(x)] for all values of x greater than zero, prove that i) Prove that for all positive integers k and m Given that uct)-cut) for c>0, prove that g(t)=L(t)/t is a constant for Vt>0 and obtain a cumulative distribution function C(x) which has the 5 marks) iv) memory-less property

Answer 1

according to HomeworkLib policy we are instructed to answer the first 4 questions