A370563 Decimal expansion of expected number of trials needed for the sum of uniform random variables from the interval [0,1] to exceed e.

6, 1, 0, 4, 0, 0, 2, 3, 4, 1, 3, 6, 3, 7, 5, 4, 1, 5, 1, 6, 6, 7, 2, 3, 2, 9, 0, 2, 2, 7, 5, 1, 4, 7, 6, 5, 9, 5, 5, 9, 1, 9, 4, 2, 6, 2, 6, 3, 3, 1, 5, 0, 2, 2, 3, 6, 6, 2, 4, 3, 5, 3, 6, 6, 3, 4, 7, 7, 3, 3, 3, 9, 7, 6, 5, 6, 6, 3, 0, 1, 9, 0, 3, 1, 6, 3

Offset: 1

Author

Clark Kimberling, May 01 2024

Keywords

• nonn
• cons

Examples

			6.104002341363754151667232902275147659559194262...
		

Links

• J. Uspensky, Introduction to Mathematical Probability (1937), 277-278.

Crossrefs

Cf. A089087, A090142.

Programs

Mathematica

u=N[E^(E - 2)*(4 + (E - 2)*E)/2, 100]; First[RealDigits[u]]
N[Mean[Table[Length[NestWhileList[# + RandomReal[1] &, 0, #1 < E &]] - 1, 10^5]]] (* sample mean *)  (* Peter J. C. Moses, Apr 30 2024 *)

Formula

Equals e*(e-2)*(4 +(e-2)*e)/2.