Topic: Mathematics
A random variable X has $\overline{X}=0$ and $\sigma_{X}^{2}=1$. Form a new random variable $Y=2X+1$. The values of $\overline{Y}$ and $\sigma_{Y}^{2}$ are
- A. 0 and 1
- B. 1 and 2
- C. 1 and 4
- D. None of above
Answer: C. 1 and 4
Explanation: Let $Y=2X+1$. $\overline{Y}=E[Y]=E[2X+1]=2E[X]+1 = 2(0)+1=1$. $\sigma_{y}^{2}=V[Y]=V[2X+1]=2^{2}V[X]=4(1)=4$.