A random signal is a time waveform that can be characterized only in some probabilistic manner. In general, it can be either a desired or undesired waveform. Any undesirable signals interferes with our desirable signal then it is called as noise.
Undesired random waveform which is said to be noise can appear in the outputs of systems in different forms. For example, In a radio astronomer's receiver, noise interferes from free space, in television system, noise will be in the form of picture interference called snow, in SONAR system, randomly generated sea sounds give rise to a noise that interferes with desired echoes. Like this, the number of random signals are limitless.
Computer bit stream will be fluctuating its values from 0 to 1 and from 1 to 0, which shows randomness. In RADAR's, signals from instruments, radio's etc random signals effect will be present. Since it is random, that is unpredictable, the concept of probability will be introduced in the concept of random variables.
Few definitions should be known before starting the concept of random variables. Those definitions are related to sets and are below.
Set: It is a collection of objects. Objects are called elements of set.
Trial: A single performance of an experiment is called a trial for which there is an outcome.
Sample space: The set of all possible outcomes in any given experiment is called sample space.
Event: Event is defined as the subset of sample space.
Mutually exclusive events: If two events have no common outcomes they are said to mutually exclusive events.
Mutually exhaustive events: It is set all outcomes of all events.
Equally likely events: If the probability of outcomes of all events are same then they are said to be equally likely.
Statistically independent events: If probability of one event is not affected by the occurrence of another event then they are said to be statistically independent.
Relative Frequency: It is average number of successes in an experiment. That is total number successful trails divided by total number of trails.
Random variable: It is a real function of the elements of a sample space S. Random variable is a function that maps all elements of sample space into points on the real line.
There are 3 types of random variables:
1. Continuous
2. Discrete
3. Mixed (Continuous + Discrete)
Conditions for a function to be a Random variable.
1. It should be single valued function.
2. P(X = inf) = P(X = -inf) = 0
Undesired random waveform which is said to be noise can appear in the outputs of systems in different forms. For example, In a radio astronomer's receiver, noise interferes from free space, in television system, noise will be in the form of picture interference called snow, in SONAR system, randomly generated sea sounds give rise to a noise that interferes with desired echoes. Like this, the number of random signals are limitless.
Computer bit stream will be fluctuating its values from 0 to 1 and from 1 to 0, which shows randomness. In RADAR's, signals from instruments, radio's etc random signals effect will be present. Since it is random, that is unpredictable, the concept of probability will be introduced in the concept of random variables.
Few definitions should be known before starting the concept of random variables. Those definitions are related to sets and are below.
Set: It is a collection of objects. Objects are called elements of set.
Trial: A single performance of an experiment is called a trial for which there is an outcome.
Sample space: The set of all possible outcomes in any given experiment is called sample space.
Event: Event is defined as the subset of sample space.
Mutually exclusive events: If two events have no common outcomes they are said to mutually exclusive events.
Mutually exhaustive events: It is set all outcomes of all events.
Equally likely events: If the probability of outcomes of all events are same then they are said to be equally likely.
Statistically independent events: If probability of one event is not affected by the occurrence of another event then they are said to be statistically independent.
Relative Frequency: It is average number of successes in an experiment. That is total number successful trails divided by total number of trails.
Random variable: It is a real function of the elements of a sample space S. Random variable is a function that maps all elements of sample space into points on the real line.
There are 3 types of random variables:
1. Continuous
2. Discrete
3. Mixed (Continuous + Discrete)
Conditions for a function to be a Random variable.
1. It should be single valued function.
2. P(X = inf) = P(X = -inf) = 0
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