$X$ and $Y$ are independent random variables with probability density functions as shown: $x$\

Question

$X$ and $Y$ are independent random variables with probability density functions as shown: $x$$0$$1$$2$ $P(X=x)$$0.2$$0.6$$0.2$ $y$$1$$2$$3$ $P(Y=y)$$0.3$$0.4$$0.3$ Construct the probability distribution of $X-Y$ and find $\mathrm{E}(X-Y)$ $\mathrm{Var}(X-Y)$

Accepted Answer

For $D=X-Y$, values $-3,-2,-1,0,1$ have probabilities $0.06,0.26,0.36,0.26,0.06$, respectively; all other values have probability zero. (a) $\mathrm{E}(X-Y)=-1$. (b) $\mathrm{Var}(X-Y)=1$.

Calculation of expected value and variance of a derived variable

Calculation of expected value and variance of a derived variable

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