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A motorcycle drives from Morayta to Lacson and back using the same course everyday. There are four stoplights on the course. Let x denote the number of red lights the motorcycle encounters going from Morayta to Lacson and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x y) is given by

A motorcycle drives from Morayta to Lacson and back using the same course everyday. There are four stoplights on the course. Let x denote the number of red lights the motorcycle encounters going from Morayta to Lacson and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x y) is given by

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A motorcycle drives from Morayta to Lacson and back using the same course everyday. There are four stoplights on the course. Let x denote the number of red lights the motorcycle encounters going from Morayta to Lacson and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by y 1 4 0.01 0.01 0.03 0.07 0.01 1 0.03 0.05 0.08 0.03 0.02 0.03 0.11 0.15 0.01 0.01 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 (a) Give the marginal probability distribution of fx (3). Answer= (b) Give the marginal probability distribution of fy (0). Answer= (c) Give the conditional density distribution of X=2 given Y = 3. Answer= (d) Give E(X). Answer= (e) Give E(Y). Answer- (f) Give E(Y| X = 3). Answer= (g) Give the standard deviation of X. Answer= *Complete the interpretation of the data. As the number of from Morayta to Lacson encountered by the motorcycle increases, the number of stoplights of its return trip tends to (increase, decrease, or be uncorrelated). Therefore, X and Y have a (zero, negative, or positive) covariance. The covariance was calculated to be (numerical value). *Describe the correlation whether a strong, a weak, or no. X and Y have correlation. What is the correlation value? = All the numerical values should be written with 2 decimal places.
Transcribed Image Text:A motorcycle drives from Morayta to Lacson and back using the same course everyday. There are four stoplights on the course. Let x denote the number of red lights the motorcycle encounters going from Morayta to Lacson and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by y 1 4 0.01 0.01 0.03 0.07 0.01 1 0.03 0.05 0.08 0.03 0.02 0.03 0.11 0.15 0.01 0.01 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 (a) Give the marginal probability distribution of fx (3). Answer= (b) Give the marginal probability distribution of fy (0). Answer= (c) Give the conditional density distribution of X=2 given Y = 3. Answer= (d) Give E(X). Answer= (e) Give E(Y). Answer- (f) Give E(Y| X = 3). Answer= (g) Give the standard deviation of X. Answer= *Complete the interpretation of the data. As the number of from Morayta to Lacson encountered by the motorcycle increases, the number of stoplights of its return trip tends to (increase, decrease, or be uncorrelated). Therefore, X and Y have a (zero, negative, or positive) covariance. The covariance was calculated to be (numerical value). *Describe the correlation whether a strong, a weak, or no. X and Y have correlation. What is the correlation value? = All the numerical values should be written with 2 decimal places.
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