Independent identically distributed random variables

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For two independent and identically distributed random variables following an exponential distribution, they must have the same lambda value. The term "identically distributed" indicates that both variables share the same distribution parameters. While Poisson random variables can have different lambda values, this does not apply to identically distributed exponential variables. Therefore, if the random variables are truly identically distributed, their lambda values will be the same. This distinction is crucial in understanding the properties of these distributions.
Somefantastik
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For two independent and identically distributed random variables having the exponential distribution, do they have the same lambda value, or are the lambda values different?
 
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If the have the same distribution function, then they both must use the same lambda.
 
I just wasn't sure b/c it looks like Poisson Random Variables can have different lambda parameters.
 
That is true.
 
Yes, they can, but your original post said "identically distributed". That doesn't mean only that the both have an exponential distribution but that they have the same exponential distribution. If they are "identically distributed" then everything about the distributions is the same.
 

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