Continuous Probability Distributions

Continuous Probability Distributions

• Uniform Distribution is a type of continuous probability distribution.
• Uniform Distribution has two key functions: Probability Density Function (PDF) and Cumulative Distribution Function (CDF).

Normal and Standard Normal Distributions

• Normal Distribution is a type of continuous probability distribution.
• Standard Normal Distribution is a special case of Normal Distribution with a mean of 0 and a standard deviation of 1.
• The Standard Normal Distribution table is used to find probabilities under the curve.
• The table provides probabilities for a given z-score (number of standard deviations from the mean).

Examples of Finding Probabilities

• Example 1: Find the probability of a Normally distributed random variable X with a population mean of 20 and a standard deviation of 6, having a value less than or equal to 28.
  • This involves finding the z-score and using the Standard Normal Distribution table to find the probability.

Normal Approximation to Binomial Distribution

• When n is large, the Binomial Distribution can be approximated using the Normal Distribution.
• A random variable X follows a Normal Distribution with a mean of np and a standard deviation of √(npq), where n is the number of trials, p is the probability of success, and q is the probability of failure.

Continuity Correction

• When approximating a discrete distribution (such as Binomial) with a continuous distribution (such as Normal), Continuity Correction is necessary.
• This correction is necessary to ensure that the approximation is accurate.