Ch 4 - 9E

Answer :

Step 1 of 2 :

Given, An analysis of sample data, the article “Pedestrians” crossing behaviors and safety at unmarked roadways in China” proposed the probability density function

f(x) = 0.15, when,  as a model for the distribution of X = time(sec) spent at the median line.

a)

The claim is to find the probability that waiting time is at most 5 sec and more than 5 sec

Let, f(x) dx  =   0.15 dx  

 Consider U =

du = -0.15dx

dx = () du

     = -6.66667 du

Therefore,    0.15 dx  =   (-6.66667)  du

                                                  = (-6.66667)  du

Here,      du =

Then,   0.15 dx = (-6.66667) +c

                                            = - 3.65875 + 6.66667

                                           = 3.00 = 3%

For more than 5

Let, f(x) dx  =   0.15 dx  

                       = 0 - (-3.65875)

                       = 3.65875