Statistics

Theory of Errors Exercise 1 : Types of Errors In the following examples, state whether the error is systematic (constant $S$) or random $R$. A 100-metre race is held in a school during a sports day. The judges start their stopwatches when the sound of the starting pistol reaches them. What type of error arises in this case? The timing of the start and end of the 100-metre race is subject to individual fluctuations, e.g. reaction time. What kind of error is it? The zero point of a voltmeter has been wrongly set. The measurements are therefore subject to an error. What kind of error is it? The resistance of a copper coil is obtained by measuring the current flowing through when a voltage is applied to it. As the coil warms up the resistance increases. What kind of error will ensue? Exercise 2 : Sample Statistics Nine different rock samples are taken from a crater on the moon whose densities are determined with the following results: $3.6, 3.3, 3.2, 3.0, 3.2, 3.1, 3.0, 3.1, 3.3 \frac{g}{cm^3}$. Calculate the mean value and standard deviation of the parent population. The velocity of a body travelling along a straight line is measured 10 times. The results are $1.30, 1.27, 1.25, 1.26, 1.29, 1.31, 1.23, 1.33, 1.24 \frac{m}{s}$. Calculate the mean value and the standard deviation. Exercise 3 : Uniform Distribution Moments A continuous random variable has the following density function: ...