Chapter 7. Special Discrete Distributions. Binomial Distribution B(n,p). Each trial results in one of two mutually exclusive outcomes. (success/failure) There are a fixed number of trials Outcomes of different trials are independent
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Special Discrete Distributions
No, probability does not remain constant
No, no fixed number
Find the discrete probability distribution
X 0 1 2 3
P(x) .125 .375 .375 .125
Out of 3 coins that are tossed, what is the probability of getting exactly 2 heads?
The number of inaccurate gauges in a group of four is a binomial random variable. If the probability of a defect is 0.1, what is the probability that only 1 is defective?
More than 1 is defective?
Binomialcdf(n,p,x) – this calculates the cumulative probabilities from P(0) to P(k)Calculator
A genetic trait of one family manifests itself in 25% of the offspring. If eight offspring are randomly selected, find the probability that the trait will appear in exactly three of them.
At least 5?
In a certain county, 30% of the voters are Republicans. If ten voters are selected at random, find the probability that no more than six of them will be Republicans.
P(x < 6) = binomcdf(10,.3,6) = .9894
In a certain county, 30% of the voters are Republicans. How many Republicans would you expect in ten randomly selected voters?
What is the standard deviation for this distribution?
What happened to the shape of the distribution as the probability of success increased?
As the probability of success increases, the shape changes from being skewed right to symmetrical at p =.5 to skewed left.
X 0 1 2 3 4
Count children until first son is born
X 1 2 3 4 . . .
What is the probability that the first son is born is at most the fourth child?
A real estate agent shows a house to prospective buyers. The probability that the house will be sold to the person is 35%. What is the probability that the agent will sell the house to the third person she shows it to?
How many prospective buyers does she expect to show the house to before someone buys the house?
This distribution deals with the probabilities of rare events that occur infrequently in space, time, distance, area, etc.
X = number of rare events per unit of time, space, etc.
l = mean value of X (Greek letter lambda)
The number of accidents in an office building during a four-week period averages 2. What is the probability there will be one accident in the next four-week period?
What is the probability that there will be more than two accidents in the next four-week period?
From 8:00 until 9:00 is a 60 minute period.
Since the period is doubled, you must double the mean amount of calls to keep it proportional!
P(X = 0) = poissonpdf(3.5,0) =.0302
Be sure to adjust l!
P(X = 0) = poissonpdf(7,0) =.0009
m = 14 &s = 3.742
l = 2 l = 4
What happens to the shape?
What happens to the means?
What happens to the standard deviations?