ONE DIMENSIONAL RANDOM VARIABLES: Handwritten notes

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  • Properties of probability

  • Distribution Function

  • Expectation Value

For the following problem by using
  1. Find the distribution function of x?
  2. What is the smallest value of x? for which probability P(X<=x)>0.5
for more click here
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Continues Random Variable

          We call the distribution function as probability density function f(x).
Properties of probability density function. click here
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Moment Generating Function (MGF)

  • Properties
  • Additional property in MGF
 for notes click here
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Bernoulli Trial

      For a single trail with only two possible results. 
Example: Tossing a coin.
p=1/2, q=1/2
p + q = 1
p = q - 1
For more than one trail, we go for Binomial Distribution

Binomial Distribution

for notes click here
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Poisson Distribution

  • In poission distribution mean and variance are same.
  • The sum of two poisson variable is poisson variable.
  • Difference between two poisson variable is not a poission variable.
for more notes click here
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Uniform Distribution  

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Exponential Distribution

          Exponential distribution is also based on time.
Memory-less property of exponential distribution.
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Geometric Distribution

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Normal Distribution

It is also called Gaussian distribution. for more click here
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Gamma Distribution

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