Discrete Distribution

1. Bernoulli distribution: any event where we only have one trial and two possible outcomes follows such a distribution.
2. The graph of a Bernoulli distribution is simple. It consists of two bars one for each of the possible outcomes, one bar would rise up to its associated probability of P and the other one would only reach 1 minus p. For Bernoulli distributions we often have to assign which outcome is 0 and which outcome is 1. After doing so we can calculate the expected value bear in mind that depending on how we assign the zero and the one our expected value will be equal to either P or 1 minus p. We usually denote the high probability with P and the lower one with one minus p. Furthermore conventially we also assign a value of 1 to the event with the probability equal to P. That way the expected value expresses the likelihood of the favorite event since we only have one trial and a favorite event we expect that outcome to occur by plugging in P and one minus p into the variance formula we find that the variance of Bernoulli events would always equal P times 1 minus that is true regardless of what the expected value is.
3. Binomial distribution is a sequence of identical Bernoulli events. Use the B to express a binomial distribution followed by the number of trials and the probability of success in each one. Therefore we read the following statement as variable X follows a binomial distribution with 10 trials and a likelihood of point six to succeed on each individual trial. Additionally, we can express Aber newly distribution as a binomial distribution with a single trial.
4. Guessing a single true or false question is a Bernoulli event.
5. Guessing the entire quiz is a binomial event.
6. The expected value of the Bernoulli distribution suggests which outcome we expect for a single trial. The expected value of the binomial distribution would suggest the number of times we expect to get a specific outcome.
7. The graph of the binomial distribution represents the likelihood of attaining our desired outcome a specific number of times if we run and trials. Our graph would consist N plus 1 many bars one for each unique value from 0 to N.
8. The Probability function: each individual trial is a newly trial so we express the probability of getting our desired outcomes as P and the likelihood of the other one as one minus p in order to get our favorite outcome. More than one way to reach our desired outcome could exist to account for this.
9. The probability function for a binomial distribution is the product of the number of combinations of picking why many elements our of N times P to the power of y times one minus p to the power of n minus Y.
10. Expected value: equals the sum of all values in the sample space multiplied by their respective probabilities.The expected value formula for a binomial event equals the probability of success for a given value multiplied by the number of trials.
11. E(Y) = p * n. This is the exact formula we need when computing the expected values for categorical variables after computing the expected value we can finally calcualte the variance.
12. Variance of Y equals the expected value of y squared minus the expected value of y squared after some simplifications. This results in end times P times 1 minus p if we plug in the values from our stock market example that gives us a variance of five times point six times point four or one point two.
13. Denote a Poisson distribution with the letters po and a single value parameter lambda. We read the statement below as variable Y follows a Poisson distribution with Lambda equal to four.
14. The Poisson distribution deals with the frequency with which an event occurs within a specific interval instead of the probability of an event the pleasant distribution requires knowing how often it occurs for a specific period of time or distance.
15. The formula of the Poisson distribution is wildly different from any other we have gone over so far. P of Y equals lambda to the power of y times the user’s number to the power of negative lambda over the y factorial.