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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.
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Is the random variable x equals 1 be stated that the random variable is discrete?
If x = 1 then X is not really a random variable but a constant.
What the deference between variable and variate?
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.
Can the Poisson distribution be a continuous random variable or a discrete random variable?
True
Define a normal random variable?
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.
How often the value of a random variable is at or below a certain value?
How often the value of a random variable is at or below a certain value.
