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 Post subject: The distribution of exp and a constantPosted: Fri, 4 May 2012 16:51:48 UTC
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Joined: Fri, 4 May 2012 16:45:00 UTC
Posts: 3
Hello,
Is there a known result about what is the distribution of the sum of constant and a exponentially distributed random variable?
If so, can someone refer me to an article or an e book with this information?
tenx
Marina

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 Post subject: Re: The distribution of exp and a constantPosted: Fri, 4 May 2012 17:22:39 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
miray wrote:
Hello,
Is there a known result about what is the distribution of the sum of constant and a exponentially distributed random variable?
If so, can someone refer me to an article or an e book with this information?
tenx
Marina

"Constant distribution"? What is that? It doesn't sound like it makes sense.

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 Post subject: Re: The distribution of exp and a constantPosted: Sat, 5 May 2012 03:07:28 UTC
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Joined: Fri, 1 Jul 2011 01:17:26 UTC
Posts: 322
miray wrote:
Hello,
Is there a known result about what is the distribution of the sum of constant and a exponentially distributed random variable?
If so, can someone refer me to an article or an e book with this information?
tenx
Marina

Do you mean Y = a + X, where X is exponentially distributed and a is a constant?

If so P(Y < y) = P(a + X < y) = P(X < y - a).

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 Post subject: Re: The distribution of exp and a constantPosted: Sun, 6 May 2012 13:13:14 UTC
 S.O.S. Newbie

Joined: Fri, 4 May 2012 16:45:00 UTC
Posts: 3
mathematic wrote:
miray wrote:
Hello,
Is there a known result about what is the distribution of the sum of constant and a exponentially distributed random variable?
If so, can someone refer me to an article or an e book with this information?
tenx
Marina

Do you mean Y = a + X, where X is exponentially distributed and a is a constant?

If so P(Y < y) = P(a + X < y) = P(X < y - a).

yes, this is what I meant.
But I need to know if Y has any known distribution. I am interested in the expectation of Y
maybe it remains exponentially distributed but with different parameter (y=a+X)? and if so where I can find the proof...

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 Post subject: Re: The distribution of exp and a constantPosted: Sun, 6 May 2012 19:07:41 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
miray wrote:
mathematic wrote:
miray wrote:
Hello,
Is there a known result about what is the distribution of the sum of constant and a exponentially distributed random variable?
If so, can someone refer me to an article or an e book with this information?
tenx
Marina

Do you mean Y = a + X, where X is exponentially distributed and a is a constant?

If so P(Y < y) = P(a + X < y) = P(X < y - a).

yes, this is what I meant.
But I need to know if Y has any known distribution. I am interested in the expectation of Y
maybe it remains exponentially distributed but with different parameter (y=a+X)? and if so where I can find the proof...

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 Post subject: Re: The distribution of exp and a constantPosted: Sun, 6 May 2012 19:35:32 UTC
 S.O.S. Newbie

Joined: Fri, 4 May 2012 16:45:00 UTC
Posts: 3
miray wrote:
mathematic wrote:
miray wrote:
Hello,
Is there a known result about what is the distribution of the sum of constant and a exponentially distributed random variable?
If so, can someone refer me to an article or an e book with this information?
tenx
Marina

Do you mean Y = a + X, where X is exponentially distributed and a is a constant?

If so P(Y < y) = P(a + X < y) = P(X < y - a).

yes, this is what I meant.
But I need to know if Y has any known distribution. I am interested in the expectation of Y
maybe it remains exponentially distributed but with different parameter (y=a+X)? and if so where I can find the proof...

You don't have to be rude. To use google you (me) have to know what you are looking for, and I believe this is what the forums for.
Tenx for your help thou, I think that solved my problem.

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 Post subject: Re: The distribution of exp and a constantPosted: Sun, 6 May 2012 20:11:29 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
miray wrote:
You don't have to be rude. To use google you (me) have to know what you are looking for, and I believe this is what the forums for.
Tenx for your help thou, I think that solved my problem.

What I googled was "sum random variables distribution formula" which is what you asked for.

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