8. Probability


PROBABILITY 
Counting techniques for the sample space 
  • State fundamental principles of counting to solve related problems 
  • State principle of permutation 
  • State principle of permutation 
  • Write the formula for permutation of n objects taken r at a time
  • Apply principle of permutation to solve related problems 
  • State principle of combination 
  • Write formula for combination of n objects taken r at a time 
  • Apply principle of combination to solve related problems 



Probability axioms and theorems 
  • State probability axioms 
  • Prove addition law of probability 
  • Prove the probability  of the complement of union and intersection of two events 
  • Use the properties of probabilities to solve related problems 
Conditional probability 
  • Define the concept of the conditional probability 
  • Calculate the conditional probability 
  • State the condition for statistical independence of two events and solve the related problems 
  • Apply conditional probability to solve problems 
Probability distributions 
  • Define a random variables 
  • Construct a probability distributions for a discrete random variable 
  • Calculate expected mean, variance and standard deviation of a discrete random variable
  • Construct a probability distribution for a continuous random variable 
  • Calculate expected mean and standard deviation of a continuous random variable 
  • Define density function and its properties 



Some special probability distributions 
  • Construct the binomial distribution 
  • Use binomial distribution to solve related problems 
  • Problems state the poisson distribution 
  • Use poisson distribution to solve the related problems 
  • State the normal distribution 
  • Apply normal distribution to solve the related problems