Suppose a widget's working lifetime (in years) is an exponential random variable with parameter = 1/2. What is the probability that the widget will keep working for another 1 year if it has been working for 3 years.
X~Exp(1/2)
E(X)=2
V(X)=4
I am stuck at this! Not too sure on how to continue. Please help!
Best Answer
Hint
If $X$ has an Exponential distribution, $$\mathbb P\{X\geq m+n\mid X\geq m\}=\mathbb P\{X\geq n\}.$$