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Continuous Random Variables

This presentation will probably involve audience discussion, which will create action items. Use PowerPoint to keep track of these action items during your presentation In Slide Show, click on the right mouse button Select “Meeting Minder” Select the “Action Items” tab

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Continuous Random Variables

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  1. This presentation will probably involve audience discussion, which will create action items. Use PowerPoint to keep track of these action items during your presentation • In Slide Show, click on the right mouse button • Select “Meeting Minder” • Select the “Action Items” tab • Type in action items as they come up • Click OK to dismiss this box • This will automatically create an Action Item slide at the end of your presentation with your points entered. Continuous Random Variables

  2. For continuous random variables we assign probabilities to intervals not points. • Total area under the curve is 1. •   = area under curve between a and b. • With continuous variables, each point has probability zero. • There is no area over a point. • P(X = a) = P(X = b) = 0

  3. Normal Distribution • One type of continuous distribution is very common, its density function is a bell-shaped curve. • This is the density of the normal distribution.

  4. Shape of the Normal Curve • The bell is symmetric about the mean of the random variable. • The standard deviation of the random variable affects the spread of the bell. • The larger the standard deviation is, the more spread out the bell.

  5. Standard Normal • The value of and characterize which normal distribution we are talking about. • The normal distribution with mean = 0 and standard deviation = 1 is called the standard normal distribution.

  6. Sampling Distribution • The probability distribution of a statistic over all possible samples is known as its sampling distribution.

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