CLASSICAL PROBABILITY.pptx

CLASSICAL PROBABILITY

1. CLASSICAL PROBABILITY

2. CLASSICAL PROBABILITY an approach to the understanding of probability based on the assumptions that any random process has a given set of possible outcomes and that each possible outcome is equally likely to occur .

3. There are three major types of probabilities: 1 . Theoretical Probability. 2. Experimental Probability. 3. Axiomatic Probability .

4. The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes . Theoretical Probability - The experimental probability of an event occurring is the number of times that it occurred when the experiment was conducted as a fraction of the total number of times the experiment was conducted Experimental Probability - Axiomatic Probability - Axiomatic Probability is just another way of describing the probability of an event. As, the word itself says, in this approach, some axioms are predefined before assigning probabilities. This is done to quantize the event and hence to ease the calculation of occurrence or non-occurrence of the event .

5. Example of Experimental Probability - Experimental probability is the results from an actual experiment of repeated trials. In class, examples are sometimes given with  coin tosses or dice rolling . For example, you could toss a coin 50 times to see the probability of getting heads (your results should come close to the theoretical probability Example of Theoretical Probability - Theoretical probability is probability that is based on an ideal situation. For instance, since  a flipped coin has two sides and each side is equally likely to land up, the theoretical probability of landing heads (or tails) is exactly 1 out of 2 . Example of Axiomatic Probability . if candidate A wins, then candidate B cannot win the elections. We know that the third axiom of probability states that, If A and B are mutually exclusive outcomes, then P (A1 ∪ A2) = P (A1) + P (A2).

6. THEORITICAL PROBABILITY In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If a random variable admits a probability density function, then the characteristic function is the Fourier transform of the probability density function .

7. Experimental Probability - Experimental probability, also known as Empirical probability, is based on actual experiments and adequate recordings of the happening of events. To determine the occurrence of any event, a series of actual experiments are conducted. Experiments which do not have a fixed result are known as random experiments .

8. Axiomatic Probability     This is done to quantize the event and hence to ease the calculation of occurrence or non-occurrence of the event .