[SOLVED] Probability and statistics (ucs410)

Experiment 5
(Continuous Probability Distributions)1. Consider that X is the time (in minutes) that a person has to wait in order to take a flight.
If each flight takes off each hour X ~ U(0, 60). Find the probability that
(a) waiting time is more than 45 minutes, and (b) waiting time lies between 20 and 30 minutes.2. The time (in hours) required to repair a machine is an exponential distributed random variable with parameter λ = 1/2.
(a) Find the value of density function at x = 3.
(b) Plot the graph of exponential probability distribution for 0 ≤ x ≤ 5.
(c) Find the probability that a repair time takes at most 3 hours.
(d) Plot the graph of cumulative exponential probabilities for 0 ≤ x ≤ 5.
(e) Simulate 1000 exponential distributed random numbers with λ = ½ and plot the simulated data.3. The lifetime of certain equipment is described by a random variable X that follows Gamma distribution with parameters α = 2 and β = 1/3.
(a) Find the probability that the lifetime of equipment is (i) 3 units of time, and (ii) at least 1 unit of time.
(b) What is the value of c, if P(X ≤ c) ≥ 0.70? (Hint: try quantile function qgamma())