Let X1,X2,⋯∼Exp(λ)X_1,X_2,\dots \sim \exponential{\lambda}X1,X2,⋯∼Exp(λ) IID. For any t>0t > 0t>0, let Nt=min{n:X1+⋯+Xn>t}N_t = \min\{n: X_1 + \dots + X_n > t\}Nt=min{n:X1+⋯+Xn>t}. Find E[Nt]\mathbb{E}\left[ N_t \right]E[Nt] when λ=2\lambda = 2λ=2 and t=4t = 4t=4.
