Statistics ch. 4-6
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what is random variable, how many types and identify them?
- "x" represents a numerical value associated with each outcome of a probability experiment
- "x" is totally by CHANCE
Two types:continuous and discrete
What is discrete random variable?
a variable that has a finite or COUNTABLE number of possible outcomes that can be listed
what is continuous random variable?
a random variable that has an UNCOUNTABLE number of possible outcomes, represented by an interval on the NUMBER LINE
What is the difference between discrete random variables and continuos random variables?
- discrete random variables represent COUNTED data
- continuous random variables represent MEASURED data
INIGHT: VALUES OF VARIABLES ROUNDING
age, height, and weight are usually rounded to the nearest year, inch, or pound
THESE ARE MEASURED DATA AND ARE CONTINUOUS RANDOM VARIABLES
what is a binomial experiment?
probability experiments that are reduced to two outcomes: success and failure
what are the conditions of binomial experiment?
- 1. repeated independent trials
- 2. two outcomes of trial: success or failure
- 3. the probability f success P(S) is the same for each trial
- 4. the random variable "x" counts the number of successful trials
What is geometric distribution?
a discrete probability distribution of a random variable "x"
what are the characteristics of geometric distribution?
- 1. trial is repeated until SUCCESS occurs
- 2. repeated trials are independent of ear other
- 3. the probability of success "p" is constant for each trial
- 4. the "x" represents the number of the trials in which the first success occurs.
- 5. the parameter of a geometric distribution is "p"
What is Poisson distribution?
a discrete probability distribution of a random variable "x''
what are the characteristics of Poisson Distribution?
- 1. the experiment consists of counting the number of times "x" an event occurs over a specified interval of time, area, or volume
- 2. the probability of the event occurring is the same for each interval
- 3. the number f occurrences in one interval is independent of the number of occurrences in other intervals
- 4. the parameter of a poisson distribution is "mu"
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