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lecture16_2slides - Statistics 528 Lecture 16 Continuous...

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Statistics 528 - Lecture 16 1 Statistics 528 - Lecture 16 Prof. Kate Calder 1 Continuous Random Variables Assigning Probabilities to Infinite Sample Spaces Consider the random variable X representing the weight you gained in the last month. What are the possible values that X can take? => there are infinite number of values X is a continuous random variable (takes values in an interval of numbers) Statistics 528 - Lecture 16 Prof. Kate Calder 2 How can we assign probabilities to events such as {1 < X < 3}? It is not possible to count the total number of outcomes that make up this event and add their probabilities because there are too many (an infinite number of) possible outcomes. We use another way of assigning probabilities to the intervals of outcomes like the above – use areas under the density curves. The probability distribution of X is described by a density curve. The probability of any event is the area under the density curve above the values of X that make up the event.
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Statistics 528 - Lecture 16 2 Statistics 528 - Lecture 16 Prof. Kate Calder 3 Recall density curves from the chapter 1: The total area under the curve is 1 and the curve always falls on or above the x-axis. The area under a density curve in any given range of values (interval) gives the proportion of observations that fall in that range. We assign
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