17-20 - Suppose the random variable X takes on the values 0, 1, and 2 with probabilities 0.2, 0.3, and 0.5, respectively. For each of the following random variables Y, find the joint distribution of X and Y, compute the covariance and the correlation, and sketch a graph showing the relationship, between X and Y that includes the range of values X =0, X = 1, and X = 2. 17. Y = 3X +1

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17-20 ▪ Suppose the random variable X takes on the values 0, 1,
and 2 with probabilities 0.2, 0.3, and 0.5, respectively. For each of
the following random variables Y, find the joint distribution of X
and Y, compute the covariance and the correlation, and sketch a
graph showing the relationship, between X and Y that includes the
range of values X = 0, X = 1, and X = 2.
17. Y = 3X + 1
9-12- For the following joint distributions, find the probabili-
ties for the random variable X - Y (the difference), and check
that E(X – Y) =E(X) – E(Y) and that Var(X – Y)= Var(X)+
Var(Y) if Cov(X, Y)=0.
9. The random variables X and Y in Exercise 1.
10. The random variables X and Y in Exercise 2, with variances
found in Section 7.2, Exercise 10.
11. The random variables X and Y in Exercise 3, with variances
found in Section 7.2, Exercise 11.
3. (from Section 7.1, Exercises 3 and 7)
X=0
X=1
X=2
Y = 1
0.1
0.2
0.3
Y = 2
0.05
0.15
0.2
PIC COLLAGE
Transcribed Image Text:17-20 ▪ Suppose the random variable X takes on the values 0, 1, and 2 with probabilities 0.2, 0.3, and 0.5, respectively. For each of the following random variables Y, find the joint distribution of X and Y, compute the covariance and the correlation, and sketch a graph showing the relationship, between X and Y that includes the range of values X = 0, X = 1, and X = 2. 17. Y = 3X + 1 9-12- For the following joint distributions, find the probabili- ties for the random variable X - Y (the difference), and check that E(X – Y) =E(X) – E(Y) and that Var(X – Y)= Var(X)+ Var(Y) if Cov(X, Y)=0. 9. The random variables X and Y in Exercise 1. 10. The random variables X and Y in Exercise 2, with variances found in Section 7.2, Exercise 10. 11. The random variables X and Y in Exercise 3, with variances found in Section 7.2, Exercise 11. 3. (from Section 7.1, Exercises 3 and 7) X=0 X=1 X=2 Y = 1 0.1 0.2 0.3 Y = 2 0.05 0.15 0.2 PIC COLLAGE
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