Theory revision 3

Bernuolli Trials 

• Random with two outcomes (success or failure)
• Random variable X often coded as 0(failure) and 1(success)
• Bernoulli trail has probability of success usually denoted p.
• Accordingly probability of failure (1-p) is ususally denoted
• q=1-p
• where x can be zero or one.
• probability of Bernoulli Distribution is;  
  

Binomial distribution

1. identical number of trials
2. the binomial distribution which consists of a fix number of statistically independent BErnoulli trials.
3. 2 possible outcome for each trials(success or failure)
4. each trial is independent(does not affect the others)
5. probability of success is the same for each trial
6. Shapes of binomial distribution
• if p<0.5: the distribution will exhibit positive skew
• if p=0.5: the distribution will be symmetirc
• if p>0.5: the distribution will exhibit negative skew

Poisson Random Variable 

• Poisson random variable represents the number of independent events that occur randomly over unit of times.
• Count number of times as event occur during a given unit of measurement.
• Number of events that occur in one unit is independent of other units.
• Probability that events occurs over given unit is identical for all units.(constant rate)
• Events occur randomly
• Expected number of events(rate) in each unit is denoted by λ(lambda)