MathDB

Problem 8

Part of 2019 LIMIT Category C

Problems(2)

floor of infinite sum

Source: LIMIT 2019 CCS1 P8

4/28/2021
The value of ⌊13!+44!+95!+…⌋\left\lfloor\frac1{3!}+\frac4{4!}+\frac9{5!}+\ldots\right\rfloor
floor functionalgebra
Poisson distro

Source: LIMIT 2019 CCS2 P8

4/28/2021
Let X1,X2,…X_1,X_2,\ldots be a sequence of independent random variables distributed exponentially with mean 11. Suppose N\mathbb N is a random variable independent of XiX_i's that has a Poisson distribution with mean λ>0\lambda>0. What is the expected value of X1+X2+…+XNX_1+X_2+\ldots+X_N? <spanclass=′latex−bold′>(A)</span> N2<span class='latex-bold'>(A)</span>~N^2 <spanclass=′latex−bold′>(B)</span> λ+λ2<span class='latex-bold'>(B)</span>~\lambda+\lambda^2 <spanclass=′latex−bold′>(C)</span> λ2<span class='latex-bold'>(C)</span>~\lambda^2 <spanclass=′latex−bold′>(D)</span> λ<span class='latex-bold'>(D)</span>~\lambda
probability