Sketch the PDF and CDF of a continuous random variable that is uniform on [0,2]

In the first hour of customers using the app they served 180 customers. STACO decided to treat this hour as 60 non-overlapping intervals of one minute each. They then assumed they could model the number of customers served each minute by independent and identically distributed Poisson Random Variables. They called the number of customers served in the ith minute X₁, so X₁ + X₂ + ... + X60 180, X₁~ Poisson(X), and X; and X, are independent if i j. - STACO used this to compute an estimated 95% confidence interval and then told Coffee Kart that they could claim to serve an average of three customers per minute. = i Recall that the maximum likelihood estimator of A is A X. Using the same assumptions as STACO and assuming that n is large enough to apply the Central Limit Theorem, calculate an estimated 95% confidence interval for X. ii Do you agree with the assumptions made by STACO. Justify your answer.

Suppose Y is a continuous random variable drawn from the uniform distributionon the interval [3, 4], that is, Y ∼ Uniform([3, 4]). Conditioned on Y = y, a second randomvariable X is drawn from the uniform distribution on the interval [0, y]. What is fX(x), thepdf of X?