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Chapter 8 - Continuous probability distributions - Coggle Diagram
Chapter 8 - Continuous probability distributions
Random variable
Assigns a numerical value to an outcome
Continuous probability distributions
Probability distributions => Continuous probability distributions =>
Uniform
Normal
Exponential
Exponential distribution
Time is a non-negative quantity
For the exponential random variable
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Probability density function
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The smaller the values of a, the flatter the curve becomes
Normal distribution
Changing____increases or decreases the spread
A normal distribution with a mean of zero and standard deviation of one is called the standard normal distribution
Changing____shifts the distribution to the left / right
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The random variable has an infinite theoretical range - infinity to + infinity
The Z distribution always has mean = 0 and standard distribution = 1
Spread is determined by the standard deviation
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Location is determined by the mean,
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Steps to find the X value for a known probability:
Find the Z value for the known probability
Convert to X values using the formula
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Empirical rules:
Mean, median and mode are equal
Evaluating normality:
Construct charts or graphs
Compute descriptive summary measures
=> Do mean, median and mode have similar values?
=> Is the interquartile range approximately 1,33
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=> Is the range approximately 6___?
Observe the distribution
Evaluate the normal probability plot
Symmetrical
Normal probability plot:
Arrange data into ordered array
Find corresponding standardised normal quartile value
Plot the pairs of points with observed data values on the vertical axis and the standardized normal quartile values on the horizontal axis.
Evaluate the plot for evidence of linearity
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Bell shaped
Uniform distributions
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Mean
A probability distribution that has equal probabilities for all possible outcomes of the random variable in intervals of equal length
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Standard deviation
Probability density functions (p.d.f)
A continuous random variable is one that can assume an uncountable number of values:
We cannot list the possible values because there is an infinite number of them
Because there is an infinite amount of values, the probability of each individual value is 0
A function f(x) is called a probability density function over the range a <=x<=b if it meets the following requirements:
f(x) >= 0 for all x between a and b; and
the total area under the curve between a and b is equal to 1
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