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. 30 40 50 30 10 20 25 Y 40 30 4 50 3 2 1 a) 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.c. X= 30), calculate the conditional PMF that Y is at most 40 minutes.

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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.
30
40
50
30
10
20
25
40
30
4
50
a) 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 PMF
that Y is at most 40 minutes.
d) What is the probability that the commuting time in cach direction on a particular day will be at least 40
minutes?
e) Determine Cov(X, Y) and the corresponding correlation coefficient px.y.
Cov(X,Y)
Recall: Cov(X,Y) = E(XY) – Hx²µy²;
Pxy =
E(XY) = Eatt x.y x y Px.x(x, y)
Transcribed Image Text: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. 30 40 50 30 10 20 25 40 30 4 50 a) 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 PMF that Y is at most 40 minutes. d) What is the probability that the commuting time in cach direction on a particular day will be at least 40 minutes? e) Determine Cov(X, Y) and the corresponding correlation coefficient px.y. Cov(X,Y) Recall: Cov(X,Y) = E(XY) – Hx²µy²; Pxy = E(XY) = Eatt x.y x y Px.x(x, y)
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