The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table. p(x, y) 1 0.010 0.015 0.025 1. 0.020 0.030 0.050 0.050 0.075 0.125 3 0.060 0.090 0.150 4. 0.040 0.060 0.100 0.020 0.030 0.050 (a) What is the probability that there is exactly one car and exactly one bus during a cycle? 0.03 (b) What is the probability that there is at most one car and at most one bus during a cycle? 0.075 (c) What is the probability that there is exactly one car during a cycle? Exactly one bus? P(exactly one car) = 0.1 P(exactly one bus) = 0.3 (d) Suppose the left-turn lane is to have a capacity of cars and one bus is equivalent to three cars. What is the probability of an overflow during a cycle? (e) Are X and Y independent rv's? Explain. O Yes, because p(x, y) = P(x) · Py(v). O Yes, because p(x, y) + p (x) · PyY). O No, because p(x, y) = Px(x) PY). O No, because p(x, y) + P(x) PY).

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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.