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# E(R)=24/11

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E(R)=24/11

Var(R)=95/121

these are the mean and variance of a four sided spinner that is represented by the discrete random variable R

find the new mean and Variance when the numbers in the spinner are trebled and then subtracted from 1

Oct 30, 2018

#1
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$$E[aX + b] = aE[X] + b\\ V[a X + b] = a^2V[X]$$

$$\tilde{R} = 1-3R\\ E[\tilde{R}] = E[1-3R] = \\ 1 - 3E[R] =\\ 1-3\left(\dfrac{24}{11}\right)=\\ 1-\dfrac{72}{11} = -\dfrac{61}{11}$$

$$V[\tilde{R}] = V[1-3R] = \\ (3)^2 V[R] = 9\left(\dfrac{95}{121}\right) = \dfrac{855}{11}$$

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Oct 30, 2018