6.1 Probability Distribution Pg. 212

Background Vocabulary Random Variable A variable whose value is determined by the outcomes of a random event Discrete Random Variable A variable that can take on only a countable number of distinct values Continuous Random Variable A variable that can take on an uncountable, infinite number of possible values, often over a specified interval Probability Distribution A function that gives the probability of each possible value of a random variable. The sum of all the probabilities in a probability distribution must equal 1.

Background Vocabulary (cont) Binomial Distribution Shows the probabilities of the outcomes of a binomial experiment Binomial (success and failure) Binomial Experiment Has n independent trials, with two possible outcomes (success or failure) for each trial. The probability for success is the same for each trial. The probability of exactly k successes in n trials is … Symmetric Distribution If a vertical line can be drawn to divide the histogram of the distribution into two parts that are mirror images Skewed If a distribution is not symmetric it is skewed

6 x 6 = 36 in the sample space Sample space for 2 Dice 11 21 31 41 51 61 12 22 32 42 52 62 13 23 33 43 53 63 14 24 34 44 54 64 15 25 35 45 55 65 16 26 36 46 56 66 11 21 31 41 51 61 12 22 32 42 52 62 13 23 33 43 53 63 14 24 34 44 54 64 15 25 35 45 55 65 16 26 36 46 56 66 6 x 6 = 36 in the sample space

Indicate the number of ways you can get a sum of the following with 2 dice. Frequency Theoretical Probability 2 3 4 5 6 7 8 9 10 11 12 11 21 31 41 51 61 12 22 32 42 52 62 13 23 33 43 53 63 14 24 34 44 54 64 15 25 35 45 55 65 16 26 36 46 56 66 1 2

Make a Probability Histogram Indicate the number of ways you can get a sum of the following with 2 dice. Make a Probability Histogram 2 4 6 8 10 12 .18 .16 .14 .12 .10 .8 .6 .4 .2 Sum Frequency Theoretical Probability 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 5 4 3 2 1

Probability of the # of Cell Phones/Household Guided Practice #1 Page 213 Probability of the # of Cell Phones/Household Dependent Variable Independent Variable

Guided Practice #1 Page 213

Binomial Distribution Success Failure

In a standard deck of cards, 25% are spades In a standard deck of cards, 25% are spades. Suppose you choose a card at random, note it is a spade, then replace it. You conduct the experiment 3 times. Draw a histogram of the binomial distribution for your experiment. n = k = p = 1 – p = P(k=0) = P(k=1) = P(k=2) = P(k=3)=

Calculator Short Cuts binompdf- Binomial Probability Distribution Function Used for the probability of k successes in n trials Type 2nd, VARS (DISTR), Down to binompdf(n,p,k) Example (3 – trials, success = 30%, 2 successes) Exactly 2 successes in 3 trials w/ 30% success can be used instead of

Calculator Short Cuts binomcdf- Binomial Cumulative Distribution Function Used for the sum of the probabilities of k successes in n trials Type 2nd, VARS (DISTR), Down to binomcdf(n,p,k) Example (3 – trials, success = 30%, k ≤ 2) 0, 1, or 2 successes in 3 trials w/ 30% success This only works for 0 to the amount of successes needed, if the problem was for greater than, just use the compliment, (1 – (P))

n = k = p = 1 – p = P(k=0) = P(k=1) = P(k=2) = P(k=3) = P(k=4) = Guided Practice #4-6 Page 214 n = k = p = 1 – p = P(k=0) = P(k=1) = P(k=2) = P(k=3) = P(k=4) = Discuss #5 and 6

n = k = p = 1 – p = P(k=0) = P(k=1) = P(k=2) = P(k=3) = P(k=4) = Guided Practice #4-6 Page 214 n = k = p = 1 – p = P(k=0) = P(k=1) = P(k=2) = P(k=3) = P(k=4) = Discuss #5 and 6

Homework Pg. 215, 1 – 15 odds Pg. 216, 1 - 17 odds