$X$ 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

The probability distribution function of $R := X - Y$ is given by $P(R = -3) = 0.06, P(R = -2) = 0.26, P(R = -1) = 0.36, P(R = 0) = 0,26, P(R = 1) = 0.06$; (a) $ -1 $ ; (b) $ 1 $.

Calculation of expected value and variance of a derived variable

Calculation of expected value and variance of a derived variable