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Probability Distributions & STATA

Probability Distributions & STATA. Katie Droll February 21, 2007. Normal Distribution. Continuous probability distribution Two Parameters: µ = mean (location parameter) σ = standard deviation (shape parameter) X is a random variable with a normal distribution X ~ N(µ, σ )

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Probability Distributions & STATA

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  1. Probability Distributions & STATA Katie Droll February 21, 2007

  2. Normal Distribution Continuous probability distribution Two Parameters: µ = mean (location parameter) σ = standard deviation (shape parameter) X is a random variable with a normal distribution X ~ N(µ, σ) Y is a random variable with a standard normal distribution Y ~ N(µ=0, σ=1)

  3. Example: from Chap 7, RE #19 The distribution of weights for the populations of males in the U.S. is approximately normal with mean=172.2 pounds, and standard deviation=29.8 pounds. • What is the probability that a randomly selected man weighs less than 130 pounds? (b) What is the probability that a randomly selected man weighs more than 210 pounds?

  4. Answer Check! Note: Homework answers should include showing all work! If you use Stata for the calculations, include your commands • P(Z < -1.42)= 0.078 (b) P(Z > 1.27)=0.102

  5. Binomial Distribution • Discrete probability distribution for a random variable with two possible outcomes • Yes/No Failure/Success • Two Parameters: • Fixed number of independenttrials: n • Constant probability of success: p n!= n*(n-1)*(n-2)*…*1

  6. Example: from Chap 7, RE #11 According to the National Health Survey, 9.8% of the population of 18 to 24-year olds in the U.S. are left-handed  • Suppose you select ten individuals from the population. In how many ways can the ten persons be ordered? (b) Without regard to order, in how many ways can you select four individuals from the group of ten? • What is the probability that exactly three of the ten persons are left-handed? • What is the probability that none of the ten persons are left-handed?

  7. Answer Check! • 10!= 3,628,800 (b) 10 choose 4= 210 • 0.055 • (0.902)10= 0.3565

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