Slides Chapter 1. Measure Theory and Probability
Slides Chapter 1. Measure Theory and Probability
Slides Chapter 1. Measure Theory and Probability
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<strong>1.</strong>5. OTHER DEFINITIONS OF PROBABILITY<br />
Selección de mujeres y anotación de su peso<br />
0.8<br />
0.7<br />
0.6<br />
0.5<br />
Frec. rel. límite<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
0<br />
1 2 3 4 5<br />
Intervalo de pesos<br />
Definition <strong>1.</strong>23 (Frequentist probability)<br />
Thefrequentist definition of probability ofaneventAisthelimit<br />
of the relative frequency of this event, when we let the number of<br />
repetitions of the r<strong>and</strong>om experiment grow to infinity.<br />
If the experiment is repeated n times, <strong>and</strong> n A is the number of<br />
repetitions in which A occurs, then the probability of A is<br />
Problems<br />
n A<br />
P(A) = lim<br />
n→∞ n .<br />
<strong>1.</strong> Check if the Laplace definition of probability satisfies the axioms<br />
of Kolmogoroff.<br />
2. Check if the frequentist definition of probability satisfies the<br />
axioms of Kolmogoroff.<br />
ISABEL MOLINA 23