Binomial Random Variable A binomial random variable X counts the number of "successes" in n independent trials, with two outcomes in each trial: success (with probability p) or failure (with …

Expected Value of a Random Variable Definition and Calculation The expected value (E [X]) is the long-term average value of a random variable, calculated as the sum of all possible values weighted by …

Random Variables: A variable that can take on different values, each with an associated probability. Probability Mass Function (PMF): A function that gives the probability that a discrete random variable …

You randomly select 3 marbles from the jar, without replacement. The random variable X represents the number of red marbles. Explain whether X is a Binomial random variable. Solution: P( first marble is …

The conditions for binomial random variables require a fixed number of independent trials with the same probability of success, while geometric random variables focus on the number of trials until the first …

A random variable that can assume any value contained in one or more intervals is called a continuous random variable. An example of a continuous random variable is the amount of time taken by a …

In fact, for a specified (non-random) number of successes (r), the number of failures (n − r) is random because the number of total trials (n) is random. For example, we could use the negative binomial …