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We consider a system composed of two subsystems placed in series. The first subsystem comprises a single component (component no. 1), whereas the second subsystem comprises two components placed in parallel. Let Skbe the lifetime of component no. k, for k = 1,2,3. We assume that the continuous random variables Sk are independent.
(a) Let N(t) be the number of system failures in the interval [0,t]. In what case(s) will the stochastic process {N(t),t ≥ 0} be a renewal process if the random variables Sk do not all have an exponential distribution? Justify.
(b) In the particular case when the variable Sk has an exponential distribution with parameter λ = 1, for all k, the process {N(t),t ≥ 0} is a renewal process. Calculate the probability density function of the time r between two consecutive renewals.
Discuss the concept of regression modelling and explain how one can assess if a statistical model fits the data well. Why is regression modelling often seen as a particularly useful form of social survey data analysis
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Construct a hypothetical 95% confidence interval for a hypothetical case
A researchers wish to estimate, with 95% confidence, the proportion of people who own a home computer. A previous study shows the 40% of those interviewed had a computer at home.
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