A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win 1.10; if they are different colors, then you win -1.10; if they are different colors ,then you win−1.00. (This is, you lose $1.00.) Calculate (a) the expected value of the amount you win; (b) the variance of the amount you win.

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SaurbHurbkj · Accepted Answer

We have that&amp;nbsp;X∈{0,1,2}&amp;nbsp;and by the nature of the problem, we have that X has Hypergeometric distribution, i.e.P(X=i)=(5i)(52−i)(102)Y=1.1⋅χ(X∈{0,2})−1⋅χ(X=1)}(a) Using the linearity of expectationE(Y)=1.1E(χ(X∈{0,2}))−E(χ(X=1))=1.1P(X=0)+1.1P(X=2)−P(X=1)=2⋅1.1⋅1045−2545=−115

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(b) Use that&amp;nbsp;Var(Y)=E(Y2)−E(Y)2. Observe that&amp;nbsp;Y2=1.12⋅χ(X∈{0,2})+12⋅χ(X=1)E(Y2)=1.21P(X=0)+1.21P(X=2)+P(X=1)=8275AnswerVar(Y)=8275−1225=4945

A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If

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