Statistics -Continuous probability distribution

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# Statistics -Continuous probability distribution - PowerPoint PPT Presentation

Statistics -Continuous probability distribution. 201 3 /11/18. Probability density function. With continuous ransom variables, the counterpart of the probability function is the probability density function, denoted by f ( x ) &lt;Note&gt; How to compute Pr ( a≤x≤b )?

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### Statistics-Continuous probability distribution

2013/11/18

Probability density function
• With continuous ransom variables, the counterpart of the probability function is the probability density function, denoted by f(x)

<Note> How to compute Pr(a≤x≤b)?

<Note>The probability of any particular value of the continuous random variable is zero.

Continuous probability distribution
• For a continuous random variable x:
• The probability distribution is defined by a probability density function, denoted by

f(x)

• The expected value of a continuous random variable is a measure of the central location for the random variable.
• The variance is used to summarize the variability in the values of a random variable.
Uniform probability distribution
• Uniform probability density function:
• Expected value for uniform probability distribution:
• Variance for uniform probability distribution:

f (x) = 1/(b – a) for a<x<b

= 0 elsewhere

E(x) = (a + b)/2

Var(x) = (b - a)2/12

Normal probability distribution
• Normal probability density function:
• Expected value for normal probability distribution:
• Variance for normal probability distribution:
Standard normal probability distribution
• Standard normal probability density function:
• Expected value for standard normal probability distribution:

0

• Variance for standard normal probability distribution:

1

Exponential probability distribution
• Exponential probability density function:
• Expected value for exponential probability distribution:
• Variance for exponential probability distribution:
Other distributions
• Chi-square distribution
• t distribution
• F distribution
• others
Relationships between distributions
• Normal distribution vs. Standard normal distribution
• Normal distribution vs. Binomial distribution
• Poisson distribution vs. Exponential distribution