Calculation of expected value and variance of a derived variable

Calculation of expected value and variance of a derived variable

IB Year 6 | Grade 12

\(X\) 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

  1. \(\mathrm{E}(X-Y)\)
  2. \(\mathrm{Var}(X-Y)\)

Solution:

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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) \(\mathrm{Var}(X-Y)=1\).

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