is any real number
= 50 and
is a random variable with
) = $20,000 and
Use Chebyshev to determine a lower bound for the probability
– $20,000| <
Note that the event in question is $10,000 < Y < $30,000.
Recall that a
you how many standard deviations a point is away from the mean; the
-score of $30,000
is ($30,000 - $20,000)/$5,477 = 1.826 and the
-score of $10,000 is ($10,000 -
$20,000)/$5,477 = -1.826.
< $30,000) = P($20,000 – 1.826($5,477) <
< ($20,000 + 1.826($5,477))
SPECIAL PROBABILITY DISTRIBUTIONS
A probability distribution is a model for the uncertainty of a random variable.
A random variable has as its outcomes a set of real numbers.
If the set of outcomes can be
listed in a table, the random variable is said to be discrete.
Continuous random variables
take values across a continuum of real numbers, perhaps, an interval.
Certain probability distributions arise so commonly in applications, that they are studied
BINOMIAL PROBABILITY DISTRIBUTIONS (DISCRETE)
GEOMETRIC DISTRIBUTIONS (DISCRETE)
HYPERGEOMETRIC PROBABILITY DISTRIBUTIONS (DISCRETE)
UNIFORM PROBABILITY DISTRIBUTIONS (CONTINUOUS)
EXPONENTIAL PROBABILITY DISTRIBUTIONS (CONTINUOUS)