Random Variables Flashcards
Explain what is meant by a discrete random variable and a continuous random variable, define the distribution function and the probability function; Define the expected value, the mean, the variance, the standard deviation, the coefficient of skewness, the moments. Derive the distribution of a function of a random variable from the distribution of the random variable.
What is a random variable?
A random variable is a function, a rule for associating a number with each element in a sample space.
So, of w is an element of the sample space S ( i.e. w is one of the possible outcomes of the experiment concerned ) and the number x is associated with this outcome, then X(w)=x where X is the random variable.
What is a discrete variable?
A random variable is discrete if the range of the function ( the set of all possible values of x ) is a finite set or a countably infinite set.
What is a probability function?
A probability function specifies how the total probability of 1 is divided up amongst the possible values of X and so gives the probability distribution of X.
What do you understand from a cumulative distribution function (CDF)?
It gives the probability that X assumes a value that does not exceed x.
What is a continuous random variable?
The range of a continuous random variable is an interval or a collection of intervals on the real line.
Probability density function for a continuous random variable
The probability associated with an interval of values (a,b) is the area under the curve of the probability density function (PDF) from a to b.
What are expected values?
Expected values are numerical summaries of important characteristics of the distribution of random variable.
