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.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
 alt="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
20
25
Y
40
5
30
4
50
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.e. X= 30), calculate the conditional PMF
that 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 40
minutes?
e) Determine Cov(X, Y) and the corresponding correlation coefficient
Px.y
Cov(X,Y)
Recall: Cov(X,Y) = E(XY) – µx²µy²;
Px.y
Е(XY) — Zail xy хурху(х,у)
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