Continuous Variable: can take on any value between two specified values. Obtained by measuring. Discrete Variable: not continuous variable (cannot take on any value between two specified values).

The total area under the curve must equal 1, representing the fact that the probability of some outcome occurring within the entire range is certain. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

Continuous random variables can take any value within a range. Unlike discrete variables, they include fractional and decimal values. These variables are often modeled using probability distributions.

The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. The chi-square distribution is often used in ...

Consider that X is the time (in minutes) that a person has to wait in order to take a flight. If each flight takes off each hour X ~ U(0, 60). Find the probability that (a) waiting time is more than ...

The Virginia Lottery offers a game called the New Year's Millionaire Raffle for which the top prize is one million dollars. There are 375,000 tickets sold, of which 508 are winners. There are three ...

Probability Distribution Notes: Probability is a fundamental aspect of mathematics that helps us understand and quantify uncertainty. Mastery of this subject is essential for students, as it has ...

A discrete random variable is a type of random variable that can take on a countable set of distinct values. Common examples include the number of children in a family, the outcome of rolling a die, ...