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| Question | Answer |
| Why is probability theory important in statistics? | Probability or “chance” plays an important role in Biology. • Many biological processes are directly affected by chance: (For example, segregation of chromosomes) • Results of experiments can also be affected by chance (chance fluctuations in the environment) • Probability models allow us to know how likely or unlikely the result of an experiment is. (When we collect data we don’t collect data from an entire population. Instead we only take a sample from a population.) |
| What is the propability (E) of an event? | the proportion of times it is expected to happen if repeated over and over again under the same conditions. Pr(E) = # ways to get outcome E Total number of outcomes |
| Addition rule | Two events where one OR the other happens can be added. When rolling a die what is the probability of getting 1 or 2 or 3 or 4 or 5? |
| What are joint or disjoint events? | disjoint= without intersection PR(E1)+PR(E2) (black hair or red hair) joint= with overlapping (What is the probability of a man having blue eyes given that he has black hair?) PR(E1)+PR(E2)- PR(E1 togehter with E2) |
| What is a conditional probability ? | propabilty of one event happening, giving that another happened. What is the probabilty of the man having blue eyes given that he has black hair PR(E1|E2)= PR (E1 together with E2) / PR (E1) |
| What are complement in probabilty | The complement of an event E consists of all the outcomes that aren’t E. • This is calculated as: Pr(Complement of E) = 1 - Pr(E) |
| What is the Multiplication rule? | The chance of two events both happen is the chance of the first multiplied by the chance of the second, given that the first event happens. (Wahrscheinlichkeits-Baum) |
| How would you calculate the probabilty of not rolling a six | Pr{E} = 1 − (5/ 6) × (5/ 6) = (11/ 36) |
| What are some probability distributions? | 1. Normal Distribution 2. Binominal distribution 3. Poisson Distribution |
| What can one say about histogramms? | discriptive statistic • Along the x axis we have ALL possible outcomes, and on the y axis we have bars that represent the probability of each outcome. The total area under a probability distribution is 1 or 100%. |
| with which parameters are normal distributions described? | the mean (denoted by μ) and the variance (denoted by σ2) X ~ N(μ,σ2) |
| What is a binominal distribution? | A variable is binomially distributed when it only has two possible outcomes. For example: • Yes (1) or No (0), |
| What are the parameters of the binominal distribution? | number of trials n, and the probability of success for each trial p. X ~ B(n,p) n =number of trials k = number of successes p= the probability of success of each trial. Pr(X = k) = (n über k) p^k(1 − p)^(n−k) |
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