Suppose $X$ is a normally distributed variable with mean 0 and variance $k$. Let $Y$ be an independent random variable taking values $-1$ and $ +1$ with equal probabilities . Define $Z$ = $XY$+$X/Y$ Find variance of Z.
My take on this.
Z=$2X$ with probability $0.5$
=$-2X$ With probability $0.5$
And i was getting VAR(Z) =4$k$