34,35,37,38

34. (1 point) 37. (1 point) Cars arriving for gasoline at a Shell station follow a Poisson The lifetimes (in months) of two types of lightbulbs are in- distribution with a mean of 7 per hour. dependent Exponential variables with means 1/1.00 and 1/0.75 A. Determine the probability that over the next hour, only respectively. one car will arrive. Probability = B. Compute the probability that in the next 6 hours, more than 29 cars will arrive Part a) Probability = Answer(s) submitted: Consider the total lifetime of the two bulbs used consecu- tively in a light fitting, so that when the first bulb expires it is immediately replaced by one of the second type. Evaluate the density function of this variable at the point 2.33, giving your (incorrect) answer to two decimal places. 35. (1 point) Let X be a random number between 0 and 1 pro- duced by the idealized uniform random number generator. Use the density curve for X, shown below, to find the probabilities: (Click on the image for a larger view.) Part b) If the mean lifetimes were equal, the total lifetime in (a) follows which type of distribution? 0.8- . A. Uniform . B. Poisson 0.6- . C. Normal . D. Exponential 0.4- . E. Gamma 0.2- 0.2 D.4 0.6 08 Answer(s) submitted: (a) P(0.1 1) = Suppose that random variable X is uniformly distributed be- B. P(X > 0.14) = tween 8 and 27. Draw a graph of the density function, and then C. P(X 27) = Answer(s) submitted