Probability distributions random variables

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1. TABLE OF CONTENT INTRODUCTION TYPES OF PD HISTROY PROBABILITY DISTRIBUTIONS EXAMPLES APPLICATIONS CONCLUDION

2. INTRPDUCTION TO PROBALITY DISTRIBUTION A probability distribution describes how probabilities are distributed over the values of a random variable. It can be thought of as a function that maps each possible value (or range of values) of the random variable to its corresponding probability.

3. TYPES OF PROBABILITY DISTRIBUTION DISCRETE PD . BINOMIAL PD .POISION PD CONTINEOUS PD . NORMAL PD

4. HISTORY Probability deals with random experiments with a known distribution, Statistics deals with inference from the data about the unknown distribution. The study of former is historically order in,for example the law of evidence while the mathematician treatment of dice began with the work of Cardano pascal, Fermiat andChristiaan between 16 th and 17 th century

5. BINOMIAL DISTRIBUTION The binomial distribution describes the probability of a fixed number of successes in a series of independent trials. Each trial has only two possible outcomes: success or failure. The number of trials in a binomial distribution is predetermined and remains constant. This allows us to calculate the likelihood of specific success rates across the set number of trials .

6. EXAMPLE APPLICATION Consider flipping a coin 10 times. The binomial distribution can tell us the probability of getting exactly 5 heads, for example. The binomial distribution is widely used in quality control, opinion polls, and clinical trials. It helps us analyze and interpret data from experiments with binary outcomes.

7. POISION DISTRIBUTION The Poisson distribution describes the probability of a certain number of events occurring within a fixed period of time or space. It's especially relevant when events happen independently of each other. The Poisson distribution requires knowing the average rate at which events happen. This average rate provides a foundation for calculating the probability of specific numbers of events.

8. EXAMPLE APPLICATION Imagine a store where customers arrive randomly throughout the day. The Poisson distribution can tell us the probability of observing a certain number of customers arriving within a given hour . The Poisson distribution finds applications in areas like queuing theory, risk management, and traffic analysis. It helps understand the likelihood of events occurring within specific timeframes.

9. NORMAL DISTRIBUTION The normal distribution, also known as the bell curve, is a continuous distribution that describes the probability of a variable taking on any value within a range. It's a symmetrical distribution with a single peak at the mean. The normal distribution is defined by its mean (average) and standard deviation (spread). These parameters determine the shape and position of the curve

10. EXAMPLE APPLICATION The heights of individuals in a large population can often be approximated by a normal distribution. This is because heights are influenced by various factors, resulting in a bell-shaped distribution around the average height. It is also used in assigning grades. Raw scores can be converted into standard scores. It is also used for developing z-scores or norms of the test. It is used to calculate the number of cases who achieve more or less than a given particular score.

11. COMPARISION

12. Understanding probability distributions is crucial for analyzing and interpreting data in various fields. By selecting the appropriate distribution based on the characteristics of the data and the research question, we can make informed decisions and draw meaningful conclusions. CONCLUSION

13. Add a Slide Title - 5 CONCLUSION Understanding probability distributions is crucial for analyzing and interpreting data in various fields. By selecting the appropriate distribution based on the characteristics of the data and the research question, we can make informed decisions and draw meaningful conclusions.