Meaning of Independent Identically distributed random variables

AI Thread Summary
Independent Identically Distributed (IID) random variables are those that are both independent and share the same probability distribution. The term "identically distributed" implies that they have the same probability density function (pdf) and cumulative distribution function (cdf), which also means they possess the same mean and variance. In the example provided, the random variables N(0,1), N(2,4), and N(3,5) are independent but not identically distributed due to differing parameters, thus they are not IID. The key takeaway is that while independence is necessary, identical distribution is crucial for the IID classification. Therefore, for random variables to be considered IID, they must have identical statistical properties.
dionysian
Messages
51
Reaction score
1
I am a little fuzzy on the meaning of Independent Identically distributed random variables. I understand the independent part but still not 100% on the identically distributed part. I understand that identically distributed means they have the same pdf and cdf but does this mean that they have the same mean and variance?

For example if i have a sequence of random variables: N(0,1),N(2,4),N(3,5) and they are all independent are they IID?
 
Physics news on Phys.org


If they have the same pdf, then they by definition have the same mean and variance.
 


For example if i have a sequence of random variables: N(0,1),N(2,4),N(3,5) and they are all independent are they IID?
They are all normal, but since the parameters are different, the distribution functions are different. (Not IID, only I).
 
Last edited:


Thanks.
 

Thread 'Value of intuitionistic logic'

I'm taking a look at intuitionistic propositional logic (IPL). Basically it exclude Double Negation Elimination (DNE) from the set of axiom schemas replacing it with Ex falso quodlibet: ⊥ → p for any proposition p (including both atomic and composite propositions). In IPL, for instance, the Law of Excluded Middle (LEM) p ∨ ¬p is no longer a theorem. My question: aside from the logic formal perspective, is IPL supposed to model/address some specific "kind of world" ? Thanks.
View full post »

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
View full post »

Similar threads

I How to show these random variables are independent?
Replies
1
Views
2K
I Randomly Stopped Sums vs the sum of I.I.D. Random Variables
Replies
2
Views
2K
I IID and Dependent RVs: A Closer Look at their Relationship and Parameters
Replies
6
Views
1K
I What is the expected (squared) coefficient of variation of a sample?
Replies
6
Views
3K
MHB Distribution and Density functions of maximum of random variables
Replies
6
Views
4K
A Sum of independent random variables and Normalization
Replies
10
Views
3K
I Random variable vs Random Process
Replies
2
Views
2K
I Linear regression and random variables
Replies
30
Views
4K
I Sampling theory and random sample
Replies
5
Views
2K
B The CDF of the Sum of Independent Random Variables
Replies
10
Views
6K

Hot Threads

Recent Insights

Back
Top