A random variable X follows the continuous uniform distribution with a lower bound of −2 and an upper bound of 4. a. What is the height of the density function f(x)? (Round your answer to 4 decimal places.)

Data are obtained on the location of incidents on a 12-kilometer-long bridge. The distribution of the distance along the bridge (in kilometers) where an incident occurs is depicted in the density curve below. 12 Distance (kilometers) along the bridge where an accident occurs 12 1. The probability of an incident that occurs in any 4 kilometers long bridge segment is always distributed over any 4-kilometer interval. A. 1/3, uniformly B. 1/3, not uniformly C. 1/6, uniformly D. 1/2, not uniformly To put it another way, the probability is 2. What is P(9 < X < 12)? 1 Same as P(2 < X < 5). 2. Same as P(2 s X < 5). 3. Same as P(2 < X < 5). 4. Same as P(2 < X < 5). A. 1 B. 1 and 2 C. 2, 3, and 4 D. 1. 2. 3, and 4

For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. f(x) = 195x, (0,5] 2, [0,5] 125 a) Find the mean. (Round to three decimal places as needed.) b) Find the standard deviation. O = (Round to three decimal places as needed.) c) Find the probability that the random variable x is within one standard deviation of the mean. The probability is. (Round to three decimal places as needed.)