The exponential is the analog of the geometric in continuous time. this problem explores the connection between exponential and geometric in more detail, asking what happens to a geometric in a limit where the bernoulli trials are performed faster and faster but with smaller and smaller success probabilities. suppose that bernoulli trials are being performed in continuous time; rather than only thinking about first trial, second trial, etc., imagine that the trials take place at points on a timeline. assume that the trials are at regularly spaced times 0,δt,2δ where δt is a small positive number. let the probability of success of each trial be λδt, where λ is a positive constant. let g be the number of failures before the first success (in discrete time), and t be the time of the first success (in continuous ) find a simple equation relating g to t. hint: draw a timeline and try out a simple example.(b) find the cdf of t. hint: first find p(t> ) show that as δt→0, the cdf of t converges to the expo(λ) cdf, evaluating all the cdfs at a fixed t≥0.