Statistics Chapter 5 - Discrete Random Variables

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  1. Random Variable
    • Always numerical
    • Represents the outcome of an experiment
    • Can be discrete or continuous
  2. Are the number of discrete random values in an experiment infinite or finite?
    Finite
  3. How long can a sequence be for a set of discrete random values?
    Infinite
  4. Are the number of continuous random values in an experiment infinite or finite?
    infinite
  5. What is the notation for a probability in a Discrete Probability Distribution?
    f(x)
  6. Why aren't values in a graphical probability distribution connected like a histogram?
    The values are discrete and there are no values in between
  7. What is the expected value of a discrete random value?
    Mean
  8. What is the mean of a discrete random variable?
    The value of x expected to occur in the long run and on average
  9. What is the Expected Value equation?
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  10. What is the Variance of a Discrete RV equation?
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  11. What is the Variance of a Discrete Random Variable (RV)?
    Average squared deviations from the expected value
  12. What are examples of binomial results?
    • 0 or 1
    • Pass or Fail
    • true or false
    • success or failure
  13. Jakob Bernoulli was a contributor of what?
    Calculus
  14. Jakob Bernoulli is known for what?
    • Ars conjectandi - The art of conjecture
    • First substantial treatise on probability
  15. What is ars conjectandi?
    Contained theory of permutation and combination  binomial theorem, multinomial theorum
  16. What are the 4 properties of a binomial experiment?
    • There are n identical trials in a series
    • Each trial has two mutually exclusive outcomes (heat/tails, success/failure)
    • Probability of success p, is constant from trial to trial
    • Outcomes are independent
  17. In a Binomial Distribution, what is our interest?
    The number of successes occurring in the n trials of a binomial experiment
  18. If you toss a coin 10 times, what is the probability of getting exactly 5 heads?
    Let x = number of successes in n trials
    • x = 5, n = 10, p = 0.5
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  19. What is the binomial probability function?
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  20. What does this part mean in the binomial probability function?
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    Number of outcomes providing exactly x successes in n trials
  21. What does this part mean in the binomial probability function?
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    Probability of a particular sequence of outcomes with x successes in n trials
  22. What can you say about a binomial distribution with the following variables?
    n = 5
    p = 0.1
    • The highest success rate would be 0
    • The lowest success rate would be 5
    • The graph is skewed right
  23. What can you say about a binomial distribution with the following variables?
    n = 5
    p = 0.5
    • The highest success values would be 2 and 3 (midpoint between 0 and 5)
    • The lowest success values would be 0 and 5
    • The graph is normally distributed
  24. What can you say about a binomial distribution with the following variables?
    n = 5
    p = 0.9
    • The success value would be 5
    • The lowest success value would be 0
    • The graph is skewed left
  25. What can you say about a binomial distribution with the following variables?
    n = 20
    p = 0.2
    • The highest success values are 3 and 4
    • The lowest success values are 11 - 20
    • The graph is highly skewed right
  26. What can you say about a binomial distribution with the following variables?
    n = 50
    p = 0.5
    • The highest success values would be around 25
    • The lowest success values would be going out from that towards the edges
    • The graph is a normal distribution
  27. What is the mean equation? (Expected value)
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  28. What is the variance equation?
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  29. What is the standard deviation equation?
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  30. If you toss a coin 100 times, what is the expected value?
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    • n = 100, p = 0.5
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  31. If you toss a coin 100 times, what is the standard deviation?
    • n = 100, p = 0.5
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  32. Of all small businesses, 27% are women-owned. In a sample of 200 small businesses, how many would you expect to be female-owned?
    • n = 200, p = 0.27
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  33. Of all small businesses, 27% are women-owned. if 8 small businesses were randomly selected, what is the probability that none are female-owned?
    • n = 8, p = 0.27, x = 0
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  34. Of all small businesses, 27% are women-owned. If 8 small businesses were randomly selected, what is the probability that half are female-owned?
    • n = 8, p = 0.27, x = 4
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Author:
honestkyle
ID:
204182
Filename:
Statistics Chapter 5 - Discrete Random Variables
Updated:
2013-04-11 16:16:12
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discrete binomial distribution stats
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Discrete Random Variables
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