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Math Help - Exponential Random Variables

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    Exponential Random Variables

    Let's say we have  n exponential random variables  X_1,X_2, \ldots, X_n . Now consider the following:  X_1 + X_2 + \ldots + X_n .

    What type of distribution would the sum of  n exponential random variables, each with mean  \lambda_i have?
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    Quote Originally Posted by shilz222 View Post
    Let's say we have  n exponential random variables  X_1,X_2, \ldots, X_n . Now consider the following:  X_1 + X_2 + \ldots + X_n .

    What type of distribution would the sum of  n exponential random variables, each with mean  \lambda_i have?
    Are the random variables continuous or discrete?

    For starters, you might want to read through this. The continuous stuff is in 7.2. This might also shed light on my reply to your hyperexponential question (if more light is needed .....)

    So work it for Z_1 = X_1 + X_2. Then use that result to get Z_2 = Z_1 + X_3. Then use that result to get Z_3 = Z_2 + X_4. etc. For a result when the random variables are discrete, read through this.
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