Probability question about uniform distribution

[habibito01]

Question
Let U₁,U₂,U₃,… be identical independent random numbers from a uniform (0,1) distribution.
Define N by N = minimum { n ∣ [MATH]\displaystyle \sum_{i=1}^n [/MATH]U_i > 1}.
Show that P(N>n) = [MATH]\frac{1}{n!}[/MATH]

I want to ask the question above, and what does "N by N = minimum { n ∣ [MATH]\displaystyle \sum_{i=1}^n [/MATH]U_i > 1} "mean?

 

[Deleted member 4993]

Question
Let U₁,U₂,U₃,… be identical independent random numbers from a uniform (0,1) distribution.
Define N by N = minimum { n ∣ [MATH]\displaystyle \sum_{i=1}^n [/MATH]U_i > 1}.
Show that P(N>n) = [MATH]\frac{1}{n!}[/MATH]

I want to ask the question above, and what does "N by N = minimum { n ∣ [MATH]\displaystyle \sum_{i=1}^n [/MATH]U_i > 1} "mean?

Have you consulted your textbook? What does it say?

 

[HallsofIvy]

Perhaps you are trying to interpret "N by N" in the sense of an "N by N square" as I did at first!

No, they are saying "Define N by the equation N= the smallest number n such that \(\displaystyle \sum_{i= 1}^n U_i> 1\)."

 

[habibito01]

I have consulted my textbook.
But, I couldn't fully comprehend the question and its solution.
Especially, P{N=n} = P{U₁+...+U_n-1 < 1, U₁+...+U_n > 1}

The following image is the solution from my textbook