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### Find the distribution of the average of exponential random variables [duplicate]

Reading my script from statistics, I have come across the following statement: Consider the following random variables $$X_1,...,X_n$$ which are all independent and identically distributed ...
3k views

### How sum of exponential variables is a gamma variable [duplicate]

I have the task to calculate $P(S_{100}\geq 200)$ where $S_{100}=\sum^{100}_{i=1} X_i$ and $X_i$, $i=1,2, \cdots, 100$ are independent $exp(\lambda)$ random variables. One method is to use the fact ...
2k views

### Relation between exponential and gamma distribution [duplicate]

If T and S are distributed exponential T,S = Exp(lambda). What is distribution T+S? The solutions says its gamma(2,lambda), but I don't understand why. I can only guess the answer by knowing that E(X+...
513 views

### Proof that $\sum_{i=1}^nX_i \sim \operatorname{Gamma}(n)$ [duplicate]

How to prove that $\sum_{i=1}^n X_i$ has a $\operatorname{Gamma}(n)$ distribution, where $X_1,\ldots,X_n$ are independent standard exponentials?
330 views

### How to use convolution formula to find distribution of $n$ exponential random variables [duplicate]

Let $W_1, W_2, \dots$ be i.i.d. exponential $(\lambda )$ variables. For each $n$, find the distribution of $T_n = W_1 + W_2 + \cdots + W_n$ I know how to deal with two i.i.d random exponential ...