A system consists of two components connected between points

A system consists of two components connected between points A and B. Let the lifetimes of these components be donated by random variable X and Y respectively that assumed to be independent random variables. Assume that the components are connected in series, let u donate the time until the system fails. What is the relationship between X,Y and U? Assume that the components are connected in parallel let the system fails. What is the relationship between X, y and V? Assume that the components are connected in a standby mode with the components whose life time is donated by X used first and the other components whose life time is donated by y used later let W donates the time until the system fails. what is the relationship between x,y and w? Assume that X is exponentially distributed with a mean of 200 hours and y is exponentially distributed with mean of 300 hours what is the PDF of v ?(recall that v measures the life time of the system when the components are connected to parallel.)

Solution

a) U =XY

b) V = 1 - (1-X)(1-Y)

c) W = X+Y

d) PDF of V =1 - (1- 200e^(-200x))(1 - 300e^(-300x))