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1. The waiting time (T) for a bicyclist before she can make a left turn at an in

ID: 1827051 • Letter: 1

Question

1. The waiting time (T) for a bicyclist before she can make a left turn at an intersection is modeled with the following probability density function (PDF): f(t)= h(2t/ 30) for30 <60seconds f(t)= 0 elsewhere a. If h is constant, compute h. b. Neatly draw and completely label the probability density function (PDF) and show (by shading on the graph) what portion of the area under the curve represents the probability that the waiting time is less than 45 seconds. Compute this probability. c. Compute the mean, ? T, and standard deviation, ? T, of T.

Explanation / Answer

a) computing value of h

the p.d.f fuction when integrated over 30 and 60 will give 1

so (int_{30}^{60} h*2*t/30 dt = 1)

(int_{30}^{60} h*1/30*2*t^2/2)

(h/30 * (60^2 - 30^2) = 1)

h = 30/(60^2 - 30^2) = 0.0111111

b)