30.47
Discrete random variable
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.
For a discrete probability distribution, you add up x*P(x) over all possible values of x, where P(x) is the probability that the random variable X takes the value x. For a continuous distribution you need to integrate x*P(x) with respect to x.
true.
The largest value minus the smallest value. In statistics, a distribution is the set of all possible values for terms that represent defined events. There are two major types of statistical distributions. The first type has a discrete random variable. This means that every term has a precise, isolated numerical value. An example of a distribution with a discrete random variable is the set of results for a test taken by a class in school. The second major type of distribution has a continuous random variable. In this situation, a term can acquire any value within an unbroken interval or span. Such a distribution is called a probability density function. This is the sort of function that might, for example, be used by a computer in an attempt to forecast the path of a weather system.
True
yes?
It is a discrete random variable.
It is a function that gives the probabilities associated with the discrete number of values that a random variable can take.
A discrete distribution is one in which the random variable can take only a limited number of values. A cumulative distribution, which can be discrete of continuous, is the sum (if discrete) or integral (if continuous) of the probabilities of all events for which the random variable is less than or equal to the given value.
The discrete random variable almost always arises in connection with counting.
That would be a discrete variable; or, in your case, it would probably be called a discrete random variable.
It could be a random variable with a discrete uniform distribution over the range 1 to 6.
Almost all statistical distribution have a mean. It is the expected value of the random variable which is distributed according to that function.
Discrete random variable
If x = 1 then X is not really a random variable but a constant.
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.