Individual A has a red die and B has a green die (both fair).If they each roll until they obtain five "doubles" (1-1,....,6-6),what is the pmf of X= the total number of times a die is rolled?What are E(X) and V(X)?

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Individual A has a red die and B has a green die (both fair).If they each roll until they obtain five &quot;doubles&quot; (1-1,....,6-6),what is the pmf of X= the total number of times a die is rolled?What are E(X) and V(X)?

Jayden-James Duffy · Accepted Answer

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Jeffrey Jordon · Accepted Answer

Probability of getting double is 16×16=136  Now let X be a random variable equal to total number of times dies rolled until they obtain five doubles  Where A and B are throwing simultaneously and both dice are fair so here the total number of rolls are 10 to obtain 5 doubles.  So the last roll must be success  pmf of X=P {9 sucesses in first (x-1) rolls} * P{last roll is success}  P(x)=(x+99)(16)9(56)x−1×56  Mean=E(X)=r(1−p)p  =100(1−16)16  V(X)=r(1−p)p2  =10(1−16)16×16  =300

Individual A has a red die and B has a green die (both fair).If they each roll until they obtain five "doubles" (1-1,....,6-6),what is the pmf of X= the total number of times a die is rolled?What are E(X) and V(X)?

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