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Continuous Random Variables and Probability Distributions - Coggle Diagram
Continuous Random Variables and Probability Distributions
Continuous Probability Distributions
a variable that can assume any value in an interval. The characteristics are exactly like continuous quantitative data.
time required to complete a task – e.g. from 35 minutes to 3 hours and 40 minutes
price of a house – RM110,000 – RM2,000,000
thickness of an item – e.g. from 5cm to 100cm
height, in inches – 42.1 – 75.06
These can potentially take on any value, depending only on the ability to measure accurately.
Probability Density Function
The probability density function, f(x), of random variable X has the following properties:
The area under the probability density function f(x) over all values of the random variable X is equal to 1.0
The probability that X lies between two values is the area under the density function graph between the two values
f(x) > 0 for all values of x
The cumulative density function F(x0) is the area under the probability density function f(x) from the minimum x value up to x0
The Normal Distribution
Symmetrical
Mean, Median and Mode
are Equal
Bell Shaped’
Location is determined by the mean, μ
Spread is determined by the standard deviation, σ
The random variable has an infinite theoretical range:
to
There are an unlimited number of normal distributions. The probability density function (area) is influenced by and which affects the shape of normal distribution.
There are an unlimited number of normal distributions. The probability density function (area) is influenced by and which affects the shape of normal distribution.
By varying the parameters μ and σ, we obtain different normal distributions.
The area (probability) covers under the normal curve will change as well
The area under the normal curve can be determined using the formula for the normal probability density function.
The Standard Normal Distribution
OUR TASK - Transform the continuous random variable distribution (x) into a unique normal distribution i.e. standard normal distribution with mean =0 and =1
The standard normal distribution is the normal distribution of the standard variable z (called “standard score” or “z-score”).
Time consuming and meaningless to find the probability for every conceivable combinations values of and for continuous random variable.
