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BE428 Lecture 5: Random Variables
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- 1what is the definition of a discrete random variable?variable that can take distinct values
- 2what is the definition of a continuous random variable?variable that can take any value in an interval
- 3what is the notation used for discrete random variables?P(X=x): the probability of the random variable X taking the value x
0 ≤ P(X=x) ≤ 1
– - 4what is the probability distribution of a discrete random variable?the list of possible values and corresponding probabilities
- 5what is the area under a probability histogram and why?since the probabilities of all possible values of the random variable must add up to 1, the total area in a probability histogram whose rectangles have width 1 must also equal 1
- 6what is the definition of the mean of a discrete random variable?the mean of a random variable is the average of all the outcomes you would expect in the long term (over all possible samples)
in general, for any discrete random variable, X with a probability distribution P, the mean of X is defined as ux - 7what is a binomial experiment?a random experiment consisting of a fixed number of repeated trials, n, that are identical and independent of each other and have only two possible outcomes
- 8what is a binomial random variable?the random variable X, that counts the number of successes in n trials is called binomial with parameters n and p
(p in this context is the probability of success in one single trial) - 9what is the binomial rule of thumb?the number of successes (X) in a sample size (n) taken without replacement from a population (proportion p) of successes is approximately binomial with n and p as long as the population size is greater than or equal to 10n
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- 4 BE428 Fichas sobre BE428 Lecture 5: Random Variables, creado por Caitlin M el 02/10/2018.
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- Caitlin M
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