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The formula, if any, depends on the probability distribution function for the variable. In the case of a discrete variable, X, this defines the probability that X = x. For a continuous variable, the probability density function is a continuous function, f(x), such that Pr(a < X < b) is the area under the function f, between a and b (or the definite integral or f, with respect to x, between a and b.

Q: What is the formula for a random variable?

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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.

True

I have included two links. A normal random variable is a random variable whose associated probability distribution is the normal probability distribution. By definition, a random variable has to have an associated distribution. The normal distribution (probability density function) is defined by a mathematical formula with a mean and standard deviation as parameters. The normal distribution is ofter called a bell-shaped curve, because of its symmetrical shape. It is not the only symmetrical distribution. The two links should provide more information beyond this simple definition.

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.

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It is a discrete random variable.

When it is random it is variable.

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.

True

random variable.

yes?

Random variables is a function that can produce outcomes with different probability and random variates is the particular outcome of a random variable.

Possible Outcomes when die is rolleddot showed by die , possible outcome in single roll1,12,13,14,15,16,1thus , formula for the probability distribution of the random variable x will beP(X=x) = x/6Cx Where as x = 1

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.

That depends on the rules that define the random variable.