Random Experiment and Sample Space
An experiment repeated under essentially homogeneous and similar conditions results in an outcome, which is unique or not unique but may be one of the several possible outcomes. When the result is unique then the experiment is called a 'deterministic' ex..
Random Experiment and Sample Space
An experiment repeated under essentially homogeneous and similar conditions results in an outcome, which is unique or not unique but may be one of the several possible outcomes. When the result is unique then the experiment is called a deterministic h..
Probability of an Event
Probability of an Event - So far, we have introduced the sample of an experiment and used it to describe events. In this section, we introduce probabilities associated to the events. If a trial results in n-exhaustive, mutually exclusive and equally likely ca..
Probability of an Event - So far, we have introduced the sample of an experiment and used it to describe events. In this section, we introduce probabilities associated to the events. If a trial results in n-exhaustive, mutually exclusive and equally likely ca..Example:
While measuring the inner radius of an open tube, using slide callipers, we get the same result by performing repeatedly the same experiment. Many scientific and Engineering experiments are deterministic. If the outcome is one of the several possible outcomes, then su..
Independent Experiment
Two random experiments are said to be independent if for every pair of events E and F, where E is associated with the first experiment and F is associated with the second experiment, the probability of simultaneous occurrence of E and F, when the two ex..
Two random experiments are said to be independent if for every pair of events E and F, where E is associated with the first experiment and F is associated with the second experiment, the probability of simultaneous occurrence of E and F, when the two ex..Note:
In an experiment if E has not occurred then E' has occurre..
Probability (continued)
Let A and B be any two events associated with a random experiment. The probability of occurrence of event A when the event B has already occurred is called the conditional probability of A when B is given and is denoted as P(A/B..
Random Variables and Probability Distributions
Random Variables and Probability Distributions - It is often very important to allocate a numerical value to an outcome of a random experiment. For example, consider an experiment of tossing a coin twice and note the number of heads (x) obtained. Outcome HH HT TH TT No..
Random Variables and Probability Distributions
It is often very important to allocate a numerical value to an outcome of a random experiment. For example, consider an experiment of tossing a coin twice and note the number of heads (x) obtained. Outcome HH HT TH TT No. of heads (x) 2 1 1 0 x is called a random variable, which..
Example:
In tossing a die experiment, what is the probability of getting at least ..
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