Question

Question #3 A video projoctor that is continuously usod has a comstant failure rate à 003/hr during its useful life. Calculate the following parameters: (a) The probability of failure within the first hour of usage: (b) The probability of failure within the first 10 hours (c) The probability of failure within the first 100 hours: (d) The probability of failure within the next 10 hours, if it has already been in use for 100 hours

Answer 1

a)P(failure witih in first hour)=P(X<1)=1-e^-$\lambda$t =1-e^-0.03*1 =0.029554

b)

P(failure with in first 10 hour)=P(X<1)=1-e^-$\lambda$t =1-e^-0.03*10 =0.259182

c)

P(failure with in first 100 hour)=P(X<1)=1-e^-$\lambda$t =1-e^-0.03*100 =0.950213

d)

here as exponential distribution is memoryless

therefore P(X<110|X>100)=P(X<10)=0.259182