Download Section 6-3 Part I

§6-3
Binomial & Geometric
Random Variables
Goals:
 Binomial settings and binomial random
variables
 Binomial probabilities
 Mean and standard deviation of a binomial
distribution
 Binomial distributions in statistical sampling
 Geometric random variables
What do these have in common?
 Toss a coin 5 times. Count the # of heads.
 Spin a roulette wheel 8 times. Record how many time the
ball lands in a red slot
 Take a random sample of 100 babies born in the US today.
Count the number of little girls.
Repeated trials of the same chance process
# of trials is fixed in advance
Trials are independent
Looking for a # of successes
Chance of success is the same for each trial
BS…Binomial Setting
 When these conditions are meet we have a binomial setting.
Definition
A binomial setting arises when we perform several
independent trials of the same chance process and record the
number of items that a particular outcome occurs.
The 4 conditions for a binomial setting are
Binary?
Independent?
Number?
Success?
BINS
“BINS”
Binary…possible outcomes can be classified as a “success”
or “failure”
Independent…the result of one trial cannot have an
effect on another trial
Number…the # of trials, n, is fixed in advance
Success…probability of success on each trial is the same
Binomial random variable &
binomial distribution
 The count X of successes in a binomial setting is a
binomial random variable.
 The probability distribution of X is a binomial
distribution with parameters n and p, where n
is the # of trials of the chance process and p is the
probability of a success on any one trial.
 The possible values of X are the whole numbers
from 0 to n.
Examples
 Type O blood….
 Turn over 10 cards record aces…
 Turn over top card, replace, repeat until …
More examples
1. Shuffle a deck of cards. Turn over the top card.
Put the card back in the deck, and shuffle again.
Repeat this process 10 times. Let X = the # of
aces you observe.
2. Choose three students at random from your
class. Let Y = the # who are over 6 feet tall.
3. Flip a coin. If it’s heads, roll a 6-sided die. If
it’s tails, roll and 8-sided die. Repeat this
process 5 times. Let W = the # of 5’s you roll.
Homework
 Page 403
 69-73 all