Skip to main content

[Community Question] Statistics: Expected value for exponential distribution not adding up

One of our user asked:

So I'm given an assignment in probability and statistics that states the following:

The download time for one document through the internet on a lab computer has an average of 25 seconds and that time has an exponential distribution. Find the expected time to download 3 documents.

So judging by the assignment if the download time for a single document has an exponential distribution then:

$\frac{1}{λ} = 25 => λ = \frac{1}{25}$

Now since we are looking for 3 documents the λ for 3 documents is equaled to:

$λ = \frac{3}{25}$

Hence the expected value should be equaled to: $\frac{25}{3}$ seconds

However here is my confusion:

Since $\frac{25}{3} < 25$ and we're talking about the expected time to download 3 files then souldn't the expected value be grater than 25?


Labels

Labels:

Comments

Post a Comment

Popular posts from this blog

[Community Question] Calculus: Manifold with boundary - finding the boundary

One of our user asked: I have the manifold with boundary $M:= \lbrace (x_1,x_2,x_3) \in \mathbb R^3 : x_1\geq 0, x_1^2+x_2^2+x_3^2=1\rbrace \cup\lbrace (x_1,x_2,x_3) \in \mathbb R^3 : x_1= 0, x_1^2+x_2^2+x_3^2\leq1\rbrace$ and I need to find the boundary of this manifold. I think it is $\lbrace (x_1,x_2,x_3) \in \mathbb R^n : x_1= 0, x_2^2+x_3^2=1\rbrace$ , the other option is that the boundary is the empty set? I think the first is right? Am I wrong?
Post a Comment
Read more

[Community Question] Linear-algebra: Are linear transformations between infinite dimensional vector spaces always differentiable?

One of our user asked: In class we saw that every linear transformation is differentiable (since there's always a linear approximation for them) and we also saw that a differentiable function must be continuous, so it must be true that all linear operators are continuous, however, I just read that between infinite dimensional vector spaces this is not necessarily true. I would like to know where's the flaw in my reasoning (I suspect that linear transformations between infinite dimensional vector spaces are not always differentiable).
Post a Comment
Read more