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Let $X sim operatornameGeo(p)$, find the probability mass function of $Y = X + 2$.

0

$begingroup$

Let $X sim operatornameGeo(p)$, find the probability mass function of $Y = X + 2$.

I did the following but I don't know if its correct.

Since X follows the geometric distribution we have that $mathbbP(X=n)=p(1-p)^n-1$.

Therefore, $mathbbP(Y=n) = mathbbP(X+2=n)=mathbbP(X=n-2)=p(1-p)^n-3$.

probability-theory

share|cite|improve this question

edited Mar 18 at 22:36

Bernard

123k741117

asked Mar 18 at 22:13

Jasper Jasper

607

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Looks good, probably best to specify the range of $n$ too (for $Y$).
  $endgroup$
  – Minus One-Twelfth
  Mar 18 at 22:18
  

  
  
  
  

add a comment | 

0

$begingroup$

Let $X sim operatornameGeo(p)$, find the probability mass function of $Y = X + 2$.

I did the following but I don't know if its correct.

Since X follows the geometric distribution we have that $mathbbP(X=n)=p(1-p)^n-1$.

Therefore, $mathbbP(Y=n) = mathbbP(X+2=n)=mathbbP(X=n-2)=p(1-p)^n-3$.

probability-theory

share|cite|improve this question

edited Mar 18 at 22:36

Bernard

123k741117

asked Mar 18 at 22:13

Jasper Jasper

607

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Looks good, probably best to specify the range of $n$ too (for $Y$).
  $endgroup$
  – Minus One-Twelfth
  Mar 18 at 22:18
  

  
  
  
  

add a comment | 

$begingroup$

Let $X sim operatornameGeo(p)$, find the probability mass function of $Y = X + 2$.

I did the following but I don't know if its correct.

Since X follows the geometric distribution we have that $mathbbP(X=n)=p(1-p)^n-1$.

Therefore, $mathbbP(Y=n) = mathbbP(X+2=n)=mathbbP(X=n-2)=p(1-p)^n-3$.

probability-theory

share|cite|improve this question

edited Mar 18 at 22:36

Bernard

123k741117

asked Mar 18 at 22:13

Jasper Jasper

607

$endgroup$

share|cite|improve this question

edited Mar 18 at 22:36

Bernard

123k741117

asked Mar 18 at 22:13

Jasper Jasper

607

share|cite|improve this question

edited Mar 18 at 22:36

Bernard

123k741117

asked Mar 18 at 22:13

Jasper Jasper

607

edited Mar 18 at 22:36

Bernard

123k741117

edited Mar 18 at 22:36

Bernard

123k741117

asked Mar 18 at 22:13

Jasper Jasper

607

asked Mar 18 at 22:13

Jasper Jasper

607