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 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 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 ...

The probability density function of a uniform random variable looks like a horizontal line segment over the support. This indicates that for any interval of a given length within the support, the ...

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 ...

The reports aim to provide a clear understanding of key concepts in probability and statistics, making them accessible to learners at all levels. Each report breaks down complex topics into digestible ...

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.