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,2Δt,..., 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 time).(a) 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>t).(c) Show that as Δt→0, the CDF of T converges to the Expo(λ) CDF, evaluating all the CDFs at a fixed t≥0.