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