The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 10 seconds. (a) Sketch this exponential probability distribution. 0.15 fx) fx) fix) 0.15 0.15 0.15 0.10 0.10 0.10 0.10 0.05 0.05 0.05 0.05 5 10 15 20 25 30 10 15 25 30 5 10 20 15 20 25 30 5 10 15 20 25 30 (b) What is the probability that the arrival time between vehicles is 10 seconds or less? (Round your answer to four decimal places.) 6321 (c) What is the probability that the arrival time between vehicles is 4 seconds or less? (Round your answer to four decimal places.) | 4512 (d) What is the probability of 32 or more seconds between vehicle arrivals? (Round your answer to four decimal places.) 0498

Find the mean of the following probability distribution. xx P(x)P(x) 0 0.1536 1 0.2644 2 0.1896 3 0.2421 4 0.1502 mean =    xx P(x)P(x) 0 0.25 1 0.15 2 0.3 3 0.3 Find the mean of this probability distribution. Round your answer to one decimal place.

The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table below. y P(xy) 1 2. 0. .025 .015 .010 .050 .030 020 2. .125 .075 050 3. 150 090 060 4. 100 .060 040 050 .030 .020 Suppose the left-turn lane is to have a capacity of six cars, and that one bus is equivalent to three cars. What is the probability of an overflow duringa cycle? Select one: O 48 O 28 O38 0.18

Benford's law, also known as the first-digit law, represents a probability distribution of the leading significant digits of numerical values in a data set. A leading significant digit is the first occurring non-zero integer in a number. For example, the leading significant digit in the number 127 is 1. Let this leading significant digit be denoted x. Benford's law notes that the frequencies of x in many datasets are approximated by the probability distribution shown in the table. 1 3 4 5 7 8 9. P(x) 0.301 | 0.176 | 0.125 | 0.097 0.079 | 0.067 0.058 0.051 | 0.046 Determine E(X), the expected value of the leading significant digit of a randomly selected data value in a dataset that behaves according to Benford's law? Please give your answer to the nearest three decimal places.