Biostatistics Examination 2 Flash Cards

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  1. Define discrete.
    A discontinuous [finite] number of outcomes.
  2. Steps for Discrete Probability Distribution:
    • 1) Define a variable.
    • 2) Create a discrete probability distribution
    • 3) Determine if the distribution is valid
    • 4) Compute the mean or expected value of x
    • 5) Compute the variance and standard deviation
  3. Define binomial distribution.
    The discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p.
  4. What would x in a discrete probability distribution problem be referred to as?
    x is called the discrete random variable.
  5. Image Upload 1
    Discrete Probability Distribution
  6. What are some properties that make a distribution valid?
    • 1) Each probability must be a fraction [0­ ≤ probability ≤ 1]
    • 2) The sum of all probabilities equal up to 1 [∑ probabilities = 1]
  7. The following formula refers to the whole population if the parameter is considered to be discrete/finite (it is used to compute the mean or expected value of x):
    μ = ∑x p(x)
  8. The following formula is used to compute the variance and/or standard deviation:
    σ² = ∑x² p(x)-μ²
  9. In discrete probability distributions, each event should be considered to be ______________________ of another.
    independent
  10. Explain what is being done with this formula:
    P(GGG)= p(G) p(G) p(G)
    The probability at each stage is being multiplied.
  11. What are the four properties of a binomial experiment?
    • 1) The experiment has been repeated more than once
    • 2) There must be only two possible outcomes
    • 3) Repetitions of the experiment must be independent of each other
    • 4) Probabilities must remain constant from trial to trial
  12. To compute the probabilities of a binomial experiment, you must use the binomial formula:
    P(x=r)=C(n,r)·pr·(1-p)(n-r)
  13. In the formula: P(x=r)=C(n,r)·pr·(1-p)(n-r), what are the p and n values?
    The n [number of trials] and p [probability of success] are called the parameters of the Binomial Distribution and must always be specified in a problem in order to work out the problem.[Note: The r can be any number greater than or equal to 0.]
  14. What does the C(n,r) represent?
    C(n,r) represents the number of ways to arrange r successes out of n trials.
  15. The combination formula:
    • C(n,r)= n!/[r!(n-r)!]
    • The (n,r) can be thought of as a coordinate plane pair (x,y). [Note: n!=n(n-1)(n-2)(n-3)...3·2·1; i.e. 0!=1, 1!=1, 2!=2·1=2, 3!=3·2·1=6, 4!=4·3·2·1=24]
  16. What are the two shortcut formulas for a binomial experiment?
    • 1) μ=np
    • 2) σ²=np(1-p)
  17. Which formula would be best to solve for the binomial number?
    μ=np
  18. Which formula would be best to solve for the variance?
    σ²=np(1-p)
  19. What determines whether an answer is usual?
    In order to be considered a usual amount, a number must fall between two standard deviations of a distribution’s mean [μ ± 2σ].
  20. What is continuous probability distribution?
    Continuous probability distribution is when a probability distribution has a cumulative distribution function that is continuous. That means, the variable x has no probability of attaining the value r, therefore its probability will have a zero value [P(x=r)=0]. The x in this case is referred to as a continuous random variable.
  21. In reference to a graph, what property of that graph is equivalent to its probability?
    A graph’s area/density/thickness can be used to determine the probability of a graph’s component(s).
  22. While a 1)_____________________ graph can be used as a continuous probability distribution, the 2)__________________________ graph is more commonly used by statisticians.
    • 1) uniform
    • 2) bell-shaped or normal distribution or Gaussian distribution or bell curve or symmetric shape [might want to know these various names]
  23. Image Upload 2
    Bell-shaped curve or normal distribution or Gaussian distribution or bell curve or symmetric shaped curve
  24. What determines whether an amount is usual in a continuous probability distribution?
    The amount must be greater than 5%.
  25. Image Upload 3
    This approach is the one approach used in determining the area of the bell-shaped curve in a calculus-based course.
  26. Image Upload 4
    The normal distribution function
  27. Which continuous probability distribution graph does Z distribution refer to?
    It refers to the standard normal distribution.
  28. What do the numbers found in the Z-score table refer to?
    The numbers found in the Z-score table refer to the probabilities to the left of a number found on a normal distribution graph.
  29. In the continuous probability distribution, what two properties are relevant?
    • 1) The sum of all probabilities must equal 1 [∑ probabilities=1]
    • 2) Zero is always in the middle of a standard normal distribution
  30. What formula should be used when converting a scale to the Z-scale?
    Image Upload 5
  31. x has a binomial distribution with the parameters 1)_________ and 2)__________.
    • 1) n
    • 2) p
    • [Note: It is written in (n,p) notation.]
  32. The y has a binomial distribution that differs in its parameters from the x distribution. What are its parameters? (Write it in the correct notation.)
    n(μ,σ²)
  33. The variables/parameters used in statistics are referred to as ________________.
    unbiased estimators
  34. Image Upload 6
    What two functions best normalize a distribution graph?
    • 1) taking the square root of x
    • 2) log x
  35. What are the six graphs viewed while assessing normality?
    • 1) Histogram
    • 2) Stem and leaf
    • 3) P-P plots
    • 4) Q-Q plots
    • 5) Skewness
    • 6) Kurtosis
  36. Of the six graphs of assessing normality, which two are used for standard normal distributions?
    The P-P plots and Q-Q plots are used when assessing the normality of a standard normal distribution plot.
  37. Of the six graphs viewed while assessing normality, which of the six is used to assess the normality of a numerical quantitative distribution?
    Kurtosis is used when assessing the normality of a numerical quantitative distribution.
  38. What is the Central Limit Theorem?
    The central limit theorem states that the mean of an independent random variable will be normally distributed [meaning that it will correlate with the standard normal distribution].
  39. Standard deviation _______________ with larger population samples.
    decreases
  40. If x has a non-normal distribution, then the rule n___30 must be applied.
  41. The formula used to compute probabilities about the mean of x:
    Image Upload 7
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Biostatistics Examination 2 Flash Cards
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Exam 2 study flash cards for the Biostatistics PHCY 4600 course taken at XUCOP.
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