A motorcycle drives from Welcome Rotonda to Fairview 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 Welcome Rotonda to Fairview 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 4 0.01 0.03 0.01 0.03 0.07 0.01 0.05 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.01 0.1 0.03 0.02 0.07 0.03 0.01 4 0.01 0.06 0.01 0.01 Find: (a) Give the marginal probability distribution of fx (0). (b) Give the marginal probability distribution of fy (3). (c) Give the conditional density distribution of X=3 given Y = 3. (d) Give E(X). (e) Give E(Y). () Give E(XI Y = 3). (9) Give the standard deviation of Y. "Complete the interpretation of the data. As the number of trip tends to from Welcome Rotonda to Fairview encountered by the motorcycle increases, the number of stoplights of its return (increase, decrease, or be uncorrelated). Therefore, X and Y have al (zero, negative, of 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? =
A motorcycle drives from Welcome Rotonda to Fairview 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 Welcome Rotonda to Fairview 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 4 0.01 0.03 0.01 0.03 0.07 0.01 0.05 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.01 0.1 0.03 0.02 0.07 0.03 0.01 4 0.01 0.06 0.01 0.01 Find: (a) Give the marginal probability distribution of fx (0). (b) Give the marginal probability distribution of fy (3). (c) Give the conditional density distribution of X=3 given Y = 3. (d) Give E(X). (e) Give E(Y). () Give E(XI Y = 3). (9) Give the standard deviation of Y. "Complete the interpretation of the data. As the number of trip tends to from Welcome Rotonda to Fairview encountered by the motorcycle increases, the number of stoplights of its return (increase, decrease, or be uncorrelated). Therefore, X and Y have al (zero, negative, of 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? =
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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NOTE: subparts a,b and c is answered already.
Transcribed Image Text:A motorcycle drives from Welcome Rotonda to Fairview 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 Welcome Rotonda to Fairview 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
1
2
4
0.01
0.01
0.03
0.07
0.01
0.03
0.05
0.08
0.15
1
0.03
0.02
2
0.03
0.11
0.01
0.01
3
0.02
0.07
0.1
0.03
0.01
4
0.01
0.06
0.03
0.01
0.01
Find:
(a) Give the marginal probability distribution of fx (0).
(b) Give the marginal probability distribution of fy (3).
(c) Give the conditional density distribution of X=3 given Y = 3.
(d) Give E(X).
.
(e) Give E(Y).
(1) Give E(X) Y = 3).
(g) Give the standard deviation of Y.
*Complete the interpretation of the data.
As the number of
from Welcome Rotonda to Fairview encountered by the motorcycle increases, the number of stoplights of its return
trip tends to
covariance was calculated to bel
*Describe the correlation whether a strong, a weak, or no.
(increase, decrease, or be uncorrelated). Therefore. X and Y have a
(zero, negative, or positive) covariance. The
(numerical value).
X and Y have
correlation.
What is the correlation value? =
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