Continuous Distribution Quiz

PDF page 350: Uniform Distribution a continuous random variable (RV) that has equally likely outcomes over the domain, a < x < b. 2

PDF page 350: memoryless property For an exponential random variable X, the memoryless property is 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 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. The probability k −λ

PDF page 352: • Memoryless Property: P(X > x + k|X > x) = P (X > k)

PDF page 350: 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 351: 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 350: 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 1 1

PDF page 350: notation is X ~ Exp(m). The mean is μ = and the standard deviation is σ = . The probability density function is

PDF page 352: Exponential: X ~ Exp(m) where m = the decay parameter

PDF page 350: 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 351: • The total area under the curve f(x) is one.

PDF page 354: 9. A continuous probability function is restricted to the portion between x = 0 and 7. What is P(x = 10)?

PDF page 366: 5 P(6 < x < 7) 7 one 9 zero 11 one 13 0.625 3 1

PDF page 350: Conditional Probability the likelihood that an event will occur given that another event has already occurred. decay parameter The decay parameter describes the rate at which probabilities decay to zero for increasing values of

PDF page 350: x. It is the value m in the probability density function f(x) = me

PDF page 355: The distribution can be written as X ~ U(1.5, 4.5).

PDF page 350: 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 351: distribution function of X is P(X ≤ x) = 1 – e .

PDF page 352: • cdf: P(X ≤ x) = 1 – e