The following case study was reported in the article “Parking Tickets and Missing Women,” which appeared in an early edition of the book Statistics: A Guide to the Unknown. In a Swedish trial on a charge of overtime parking, a police officer testified that he had noted the position of the two air valves on the tires of a parked car: To the closest hour, one was at the one o’clock position and the other was at the six o’clock position. After the allowable time for parking in that zone had passed, the policeman returned, noted that the valves were in the same position, and ticketed the car. The owner of the car claimed that he had left the parking place in time and had returned later. The valves just happened by chance to be in the same positions.
An “expert” witness computed the
a. What reasoning did the expert use to arrive at the probability of 1/144?
b. Can you spot the error in the reasoning that leads to the stated probability of 1/144?
c. What effect does this error have on the probability of occurrence?
d. Do you think that 1/144 is larger or smaller than the correct probability of occurrence?
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Introduction to Statistics and Data Analysis
- Let X be a random variable with support SX = {−3, 0.5, 3, −2.5, 3.5}. Part ofits probability mass function (PMF) is given bypX(−3) = 0.15, pX(−2.5) = 0.3, pX(3) = 0.2, pX(3.5) = 0.15.(a) Find pX(0.5).(b) Find the cumulative distribution function (CDF), FX(x), of X.1(c) Sketch the graph of FX(x).arrow_forwardA well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected. a) Calculate the percentage of components that get rejected. b) In a manufacturing run of 1000 units, how many are expected to be rejected? c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.arrow_forward5. Let X and Y be independent random variables and let the superscripts denote symmetrization (recall Sect. 3.6). Show that (X + Y) X+ys.arrow_forward
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- 1. Show, by using characteristic, or moment generating functions, that if fx(x) = ½ex, -∞0 < x < ∞, then XY₁ - Y2, where Y₁ and Y2 are independent, exponentially distributed random variables.arrow_forward1. Show, by using characteristic, or moment generating functions, that if 1 fx(x): x) = ½exarrow_forward1990) 02-02 50% mesob berceus +7 What's the probability of getting more than 1 head on 10 flips of a fair coin?arrow_forward
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