The longevity of Solan's motorized vehicles (in years), is \(T \sim f(x)=\) weib \(_{(1,0.5)}(x)\).

(a) What are \(\mu_{T}\) and \(\sigma_{T}^{2}\) ?

(b) What is the probability that a given motorized vehicle lasts for more than one year?

(c) Write down \(f(x)\) as simplified as possible. You will then see that the lifetime distribution of the vehicles is a special case of the Weibull distribution, which is also known under another name. Which probability distribution is this? And what are the parameter(s)?

The continuous uniform distribution has been omitted as a section so that the student should have at hand a tractable probability distribution to build up and study its properties. The first assignment is the key.