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).

School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York, USA. There are commonly used, continuous probability distributions of one variable, such as the normal ...

Abstract: In this chapter, we introduce the concept of a random variable and develop the procedures for characterizing random variables, including the cumulative distribution function, as well as the ...

theorem 1.3 $text{If } A = A_1 \cup A_2 \cup \cdots \cup A_m \text{ and } A_i \cap A_j = \emptyset \text { for all } i \neq j \text{ , then }$ Definition 1.1 Outcome ...

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 ...

On a certain track team, the runners all take between 4 and 7 minutes to finish a mile. Suppose the probability density function for the length of time it takes a ...