4. "Time headway" In highway traffic flow the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point is called time headway. Now, let X = the time headway for two randomly chosen consecutive cars on a highway during a period of heavy traffic flow. The following probability density function of X is suggested by traffic experts: f(x) = 0.15*e-0.15*(x-0.5) for (x ≥ 0.5 sec) 0 otherwise a. Draw f(x) from x = 0 to x= 10 sec. b. Find P(X ≤ 5 sec) and show it on the figure you have drawn. c. What is E[X] and Var[X] ? d. Find Cumulative Distribution Function of X.

The graph to the right is the uniform probability density function for a friend who is x minutes late. ​(a) Find the probability that the friend is between 20 and 30 minutes late. ​(b) It is 10 A.M. There is a 10​% probability the friend will arrive within how many​ minutes?             01020301/300Time (min)Density      X         A probability density function has a horizontal axis labeled "X" and "Time (minutes)" from 0 to 35 in intervals of 5 and a vertical axis labeled "Density" from 0 to one thirtieth. The probability density function is a rectangle from 0 to 30 with a height of one thirtieth. ​(a) The probability that the friend is between 20 and 30 minutes late is nothing.

Y is continuous random variable with the probability density function pictured. What is the probability that Y is between three and four?

Which of the following tables shows a valid probability density function? Select all correct answers. Select all that apply: x P(X=x) 0 14 1 38 2 38   x P(X=x) 0 18 1 18 2 34   x P(X=x) 0 −310 1 110 2 15 3 1   x P(X=x) 0 0.74 1 0.0 2 0.54   x P(X=x) 0 110 1 15 2 35   x P(X=x) 0 0.18 1 0.76 2 0.0