Exercises for Question Type 8: For given values of either summary statistic, finding another corresponding value using properties - IB | RevisionDojo

IB
Question Type 8: For given values of either summary statistic, finding another corresponding value using properties

Question Type 8: For given values of either summary statistic, finding another corresponding value using properties Exercises

Question 1

Given $E(X)=5$ , $E(Y)=-1$ , and $\text{Cov}(X,Y)=2$ , find $E(XY)$ .

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Question 2

Given $\text{Var}(X)=4$ , find the standard deviation of $0.5X$ .

Question 3

Given $E(X)=1$ and $E(Y)=2$ , find $E(4X - 5Y + 3)$ .

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Question 4

Given $\text{E}(X)=-3$ and $\text{Var}(X)=2$ , find $\text{Var}(X + 5)$ .

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Question 5

Given $E(X)=0.7$ and $E(X^2)=0.9$ , find $\text{Var}(2X)$ .

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Question 6

Given $\text{Var}(X)=6$ , $\text{Var}(Y)=9$ and $\text{Cov}(X,Y)=5$ , find $\text{Cov}(2X - Y, 3X + 4Y)$ .

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Question 7

Given $\text{Var}(X)=9$ , $\text{Var}(Y)=16$ , and $\text{Cov}(X,Y)=6$ , find $\text{Var}(2X - 3Y)$ .

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Question 8

Given $\operatorname{E}(X)=0$ and $\operatorname{Var}(X)=1$ , find $\operatorname{Var}\left(\frac{X+2}{3}\right)$ .

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Question 9

Given $E(X)=2$ and $\text{Var}(X)=3$ , find $E(X^2)$ .

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Question 10

Given $E(X)=5$ , find $E(3X - 2)$ .

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Question 11

Given $\text{Var}(X)=9$ , $\text{Var}(Y)=16$ , and $\text{Cov}(X,Y)=6$ , find $\text{Var}(X+Y)$ .

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Question 12

Given $\text{Var}(X)=4$ , find $\text{Var}(3X + 1)$ .

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