Problem 1: (6 Points) Consider a state-of-the-art component with a Weibull distribution having shape parameter 1.5 and scale parameter 8000 (units in hours). The function to be performed by this component is contractually specified to have a 5000h reliability of 0.94. Thus, redundancy will have to be employed, say by putting components in parallel. Using MCS determine the least number of redundant components to be used in order to reach that reliability. Replicate 10,000 times and determine the number of required components (original + redundant parts), then determine the average reliability and plot a histogram of the resulting 10,000 reliability values.

Which is the graph of the piecewise function f(x)? f(x)=[tex]f(x) = \left \{ {{-x+1, x\leq 0 } \atop {x+1, x\ \textgreater \ 0}} \right.[/tex]

What is the x-intercept and y-intercept of the equation 2x+1. 2o

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?