4. A person's commuting time from home to the workplace (X) and from the workplace to home (Y) is studied for 100days. Assume that the commuting time each way can be approximated as 30, 40, or 50 minutes. The following tableshows the number of days for each combination of X and Y.X30405030102025Y4053045021a) Plot the joint PMF of X and Y.b) Plot the marginal PMF of X and Y.c) Considering 30 minutes commuting time from home to workplace (i.e. X= 30), calculate the conditional PMFthat Yis at most 40 minutes.d) What is the probability that the commuting time in each direction on a particular day will be at least 40minutes?e) Determine Cov(X, Y) and the corresponding correlation coefficientPx.yCov(X,Y)Recall: Cov(X,Y) = E(XY) – µx²µy²;Px.yЕ(XY) — Zail xy хурху(х,у)og oy

As per bartleby guidlines, for more than three subparts, first three needs to be solved and others…

4. A person's commuting time from home to the workplace (X) and from the workplace to home (Y) is studied for 100 days. Assume that the commuting time each way can be approximated as 30, 40, or 50 minutes. The following table shows the number of days for each combination of X and Y. X 30 40 50 30 10 25 Y 40 5 4 50 3 1 a) Plot the joint PMF of X and Y. 20 30 2.

4. A person's commuting time from home to the workplace (X) and from the workplace to home (Y) is studied for 100 days. Assume that the commuting time each way can be approximated as 30, 40, or 50 minutes. The following table shows the number of days for each combination of X and Y. X 30 40 50 30 10 25 Y 40 5 4 50 3 1 a) Plot the joint PMF of X and Y. 20 30 2.

A First Course in Probability (10th Edition)

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...

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