Please show and explain the steps! Solve only (a), (b), and (c)! There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the commuter must stop on his way to work, and X, be the number of lights at which he must stop when returning from work. Suppose that these two variablesare independent, each with the pmf given in the accompanying table (so X,, X, is a random sample of size n = 2).X112P(x,) | 0.4 0.2 0.4u = 1, o2 = 0.8(a) Determine the pmf of T, = X, + X2.to134P(t,)(b) Calculate uTHow does it relate to u, the population mean?2(c) CalculateHow does it relate to o?, the population variance?2g2(d) Let X, and X, be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. Wwith T, = the sum of all four X,'s, what now are the values of E(T) and V(T,)?E(T,) =V(T.) =(e) Referring back to (d), what are the values of P(T, = 8) and P(T, 2 7) [Hint: Don't even think of listing all possible outcomes!]P(T, = 8) =P(T, 2 7) =

It is a basic application of probability . It is widely used in statistics . x1 0 1 2 P(x1)…

Answered: Please show and explain the steps!…

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...