Consider an unfair die, where the probability of obtaining 6 is p ne 1/6. The die is thrown several times. Call T the RV that counts the number of throws before a 6 appears for the first time. What will be the distribution of T.

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2022-08-28

Probability, geometric distribution definitions
Consider an unfair die, where the probability of obtaining 6 is p 1 / 6.. The die is thrown several times. Call T the RV that counts the number of throws before a 6 appears for the first time. What will be the distribution of T.

Answer & Explanation

Jonathan Bailey

Jonathan Bailey

Beginner2022-08-29Added 10 answers

Step 1
Pr ( T > t ) = Pr ( No 6 appears in the first  t  trials. ) = ( 5 6 ) t .
Pr ( T = t ) + Pr ( T > t ) = Pr ( T > t 1 ) .
Step 2
Pr ( T = t ) + ( 5 6 ) t = ( 5 6 ) t 1 .
Pr ( T = t ) = ( 5 6 ) t 1 ( 5 6 ) t = ( 5 6 ) t 1 ( 1 5 6 ) .

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