Q: What does the random variable (r) for a binomial experiment of n trials represent?

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· A variable whose values are determined by the outcomes of a random experiment is called a random variable. A random variable is a discrete random variable if it can assume values, which are finite or countable infinite. For example, tossing of a die is a random experiment and its outcomes 1, 2, 3, 4, 5 and 6 are discrete random variable. When a coin is tossed, its outcomes head and tail are discrete random variable. Three coins are thrown; the number of heads is example of discrete random variable. Note that the outcomes need ot be integers or even numbers (eg colour of eyes). · If a random variable can assume every possible value in an interval [a, b], a< b, where a and b may be - infinity and + infinity respectively, for example, the points on number line between 0 and 1; Value of 'x' between 0 and 2; Number of heads on a coin when it is tossed infinite times.

If x = 1 then X is not really a random variable but a constant.

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.

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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.

The number of 6s in 37 rolls of a loaded die and binomial.

A probability distribution describes the likelihood of different outcomes in a random experiment. It shows the possible values of a random variable along with the probability of each value occurring. Different probability distributions (such as uniform, normal, and binomial) are used to model various types of random events.

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an experiment to test a scientific hypothesis in which the variable component is controlled, not random, eg In an experiment that measures volume vs time to boiling, the volume, being the indirect variable, is measured.

Expected value of a random variable requires that the random variable can be repeated in experiment indefinitely. If the random variable can only be repeated finite times, e.g. once, there is an inadequacy of the expected value principle for a decision maker.

It is a discrete random variable.

Diameter is a continuous random variable

· A variable whose values are determined by the outcomes of a random experiment is called a random variable. A random variable is a discrete random variable if it can assume values, which are finite or countable infinite. For example, tossing of a die is a random experiment and its outcomes 1, 2, 3, 4, 5 and 6 are discrete random variable. When a coin is tossed, its outcomes head and tail are discrete random variable. Three coins are thrown; the number of heads is example of discrete random variable. Note that the outcomes need ot be integers or even numbers (eg colour of eyes). · If a random variable can assume every possible value in an interval [a, b], a< b, where a and b may be - infinity and + infinity respectively, for example, the points on number line between 0 and 1; Value of 'x' between 0 and 2; Number of heads on a coin when it is tossed infinite times.

When it is random it is variable.

Assuming you mean random variable here. A random variable is term that can take have different values. for example a random variable x that represent the out come of rolling a dice, that is x can equal 1,2,3,4,5,or 6. Think of probability distribution as the mapping of likelihood of the out comes from an experiment. In the dice case, the probability distribution will tell you that there 1/6 the time you will get 1, 2,3....,or 6. this is called uniform distribution since all the out comes have that same probability of occurring.