In distributed computing, any given task is split into smaller subtasks which are handled by separate subtasks which are handled by separate processors (which are then re-combined by a multiplexer). Consider a distributed computing system with 4 processors, and suppose for one particular purpose that pdf of completion time for a particular subtask (microseconds) on any one of the processors is given by ƒ(x) = 20 = (3x²) for 4 ≤ x ≤ 10 and = 0 otherwise. That is, the subtask completion times X₁, X₂, X₃, X₄ of the four processors each have the specified pdf.
a. Write a program to simulate the above pdf using the inverse cdf method.
b. The overall time to complete any task is the largest of the four subtask completion times: if we call this variable Y, then Y = max(X₁, X₂, X₃, X₄). (We assume that the multiplexing time is negligible.) Use your program in part (a) to simulate 10,000 values of the rv Y. Create a histogram of the simulated values of Y, and also use your simulation to estimate both E(Y) and σ_Y.