Two dice are thrown simultaneously. It X is the digit on first dice and Y is the digit on second dice, then find E(X+Y) and Var(X+Y)
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Here, X represents the number of sixes obtained when two dice are thrown simultaneously. Therefore, X can take the value of 0, 1, or 2.
∴P(X=0)=P(notgettingsixonanyofthedice)=
36
25
P(X=1)=P(sixonfirstdieandnosixonseconddie)+P(nosixonfirstdieandsixonseconddie)
=2(
6
1
×
6
5
)=
36
10
P(X=2)=P(sixonboththedice)=
36
1
Therefore, the required probability distribution is as follows.
Then, expectation of X=E(X)=∑X
i
P(X
i
)
=0×
36
25
+1×
36
10
+2×
36
1
=
3
1
=0.33
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