Question

7. Two dice are thrown simultaneously. If X denotes the number of two, find the expectation, variance & standard deviation of X​

Answer 1

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Question



Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.

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Solution



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Correct option is

A

0.33

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)=3625

P(X=1)=P(sixonfirstdieandnosixonseconddie)+P(nosixonfirstdieandsixonseconddie)

=2(61×65)=3610

P(X=2)=P(sixonboththedice)=361

Therefore, the required probability distribution is as follows.

Then, expectation of X=E(X)=∑XiP(Xi)

=0×3625+1×3610+2×