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Does a discrete random variable have to take on a positive value?
A discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,…….. Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete.
What is the expectation of a discrete random variable?
For a discrete random variable the expected value is calculated by summing the product of the value of the random variable and its associated probability, taken over all of the values of the random variable.
How do you find the ex of a discrete random variable?
E(X) = p · 1 + (1 − p) · 0 = p. Important: This is an important example. Be sure to remember that the expected value of a Bernoulli(p) random variable is p.
When is the expected value of a random variable indentical?
For a discete random variable, this means that the expected value should be indentical to the mean value of a set of realizations of this random variable, when the distribution of this set agrees exactly with the associated probability mass function (presuming such a set exists).
When to be interested in a random variable?
When a large collection of numbers is assembled, as in a census, we are usually interested not in the individual numbers, but rather in certain descriptive quantities such as the average or the median. In general, the same is true for the probability distribution of a numerically-valued random variable.
Which is an example of a variable with no expectation?
Thus, Y has no expectation. This example is called the . The fact that the above sum is infinite suggests that a player should be willing to pay any fixed amount per game for the privilege of playing this game. The reader is asked to consider how much he or she would be willing to pay for this privilege.
Is the expectation of a random variable a linear operator?
In particular, the following theorem shows that expectation preserves the inequality and is a linear operator. Theorem 1 (Expectation) Let X and Y be random variables with finite expectations. 1. If g(x) ≥ h(x) for all x ∈ R, then E[g(X)] ≥ E[h(X)].