Continuous Distribution Quiz

PDF page 364: uniform distribution a continuous random variable (RV) that has equally likely outcomes over the domain, a < x < b. Notation—X ~ U(a,b). 2

PDF page 364: exponential distribution a continuous random variable (RV) that appears when we are interested in the intervals of time between some random events, for example, the length of time between emergency arrivals at a hospital; the notation is X ~ Exp(m).

PDF page 365: If X has a uniform distribution where a < x < b or a ≤ x ≤ b, then X takes on values between a and b (may include a and a + b . The standard deviation of X is

PDF page 365: b). All values x are equally likely. We write X ∼ U(a, b). The mean of X is μ =

PDF page 364: The probability density function (pdf) is used to describe probabilities for continuous random variables. The area under the density curve between two points corresponds to the probability that the variable falls between those two values. In other words, the area under the density curve between points a and b is equal to P(a < x < b). The cumulative distribution function (cdf) gives the probability as an area. If X is a continuous random variable, the probability density function (pdf), f(x), is used to draw the graph of the probability distribution. The total area under the graph of f(x) is one. The area under the graph of f(x) and between values a and b gives the probability P(a < x < b).

PDF page 366: • The total area under the curve f(x) is one.

PDF page 364: The probability density function (pdf) is used to describe probabilities for continuous random variables. The area under the density curve between two points corresponds to the probability that the variable falls between those two values. In other words, the area under the density curve between points a and b is equal to P(a < x < b). The cumulative distribution function (cdf) gives the probability as an area. If X is a continuous random variable, the probability density function (pdf), f(x), is used to draw the graph of the probability distribution. The total area under the graph of f(x) is one. The area under the graph of f(x) and between values a and b gives the probability P(a < x < b).

PDF page 364: memoryless property for an exponential random variable X, the statement that knowledge of what has occurred in the past has no effect on future probabilities This means that the probability that X exceeds x + k, given that it has exceeded x, is the same as the probability that X would exceed k if we had no knowledge about it. In symbols we say that P(X > x + k|X > x) = P(X > k). Poisson distribution a distribution function that gives the probability of a number of events occurring in a fixed interval of time or space if these events happen with a known average rate and independently of the time since the last event; if there is a known average of λ events occurring per unit time, and these events are independent of each other, then the number of events X occurring in one unit of time has the Poisson distribution. k −λ

PDF page 366: • Memoryless property: P(X > x + k|X > x) = P (X > k)

PDF page 364: exponential distribution a continuous random variable (RV) that appears when we are interested in the intervals of time between some random events, for example, the length of time between emergency arrivals at a hospital; the notation is X ~ Exp(m).

PDF page 365: The probability P(c < X < d) may be found by computing the area under f(x), between c and d. Since the corresponding area is a rectangle, the area may be found simply by multiplying the width and the height.

PDF page 365: The cumulative distribution function (cdf) of X is defined by P (X ≤ x). It is a function of x that gives the probability that the random variable is less than or equal to x.

PDF page 365: distribution function of X is P(X ≤ x) = 1 – e .

PDF page 366: • cdf: P(X ≤ x) = 1 – e

PDF page 366: • standard deviation σ = μ

PDF page 368: 9. A continuous probability function is restricted to the portion between x = 0 and 7. What is P(x = 10)?

PDF page 380: 5 P(6 < x < 7) 7 one 9 zero 11 one 13 0.625 3 1