The expected value is the long-run average value of repetitions of the experiment it represents.
apex: false
No. The mean is the expected value of the random variable but you can also have expected values of functions of the random variable. If you define X as the random variable representing the result of a single throw of a fair die, the expected value of X is 3.5, the mean of the probability distribution of X. However, you play a game where you pay someone a certain amount of money for each throw of the die and the other person pays you your "winnings" which depend on the outcome of the throw. The variable, "your winnings", will also have an expected value. As will your opponent's winnings.
continuous random variable
Follow these steps:Find all the values that the random variable (RV) can take, x.For each x, find the probability that the RV takes than value, p(x).Multiply them: x*p(x).Sum these over all possible values of x.The above sum is the expected value of the RV, X.
A random variate is a particular outcome of a random variable: the random variates which are other outcomes of the same random variable would have different values.
A random variable is a variable which can take different values and the values that it takes depends on some probability distribution rather than a deterministic rule. A random process is a process which can be in a number of different states and the transition from one state to another is random.
A random variable which can take qualitative values rather than numeric values. For example, the question "What colour are your eyes?" will generate qualitative answers.
A discrete random variable is a variable that can only take some selected values. The values that it can take may be infinite in number (eg the counting numbers), but unlike a continuous random variable, it cannot take any value in between valid results.
That would be a discrete variable; or, in your case, it would probably be called a discrete random variable.
the range of values of a random variable.
A random variable is a function that assigns unique numerical values to all possible outcomes of a random experiment. A real valued function defined on a sample space of an experiment is also called random variable.
It can take only a finite number of values. These need not be integer values.
true.