John, an aspiring physics student, works part-time parking cars at a down town h

Question

John, an aspiring physics student, works part-time parking cars at a down town hotel. The lot is a long, underground tunnel, with all the cars parked in a single long row, 600 m long. When owners return for their cars, instead of telling them exactly where to find their cars, he describes the location in terms of probability and probability density. (a) Mr. Vanderbilt is told that his car "could be anywhere in the lot." which means that the probability density is constant. Calculate the value of this uniform probability density P(x) for Mr. Vanderbilt to find his car a distance x from one end of the lot. (Answer in units of probability/m.) (b) Find the probability that Mr. Vanderbilt's car is in the first 100 m of the lot. (c) Mrs. Reeve is told that the probability density to find her car is a constant P_1 from x = 0 to x = 200 m, and a second constant P_2 = P_1/3 in for x = 200 to x = 600 m. Find the different constant probability densities P_1 for 0

Explanation / Answer

a) pr(Vanderbilt find her car at x distance ) = 1/600 0<x<600
b)100/600=1/6
c)p1+p2=1 p1=3p2.
so, 4p2=1. =>p2=0.25

p1=0.75

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