2095337
| Question | Answer |
| What are the conditions of a binomial distribution? | A fixed number of independant, success or failure trialswith a constant probability of sucess. |
| What is E(X) for binomial distributions? | np |
| What is Var(X) for Binomial distributions? | np(1-p) |
| What is the mean and varience of a Poisson distribution? | lambda for both |
| What can 'n' in a binomial distribution also be called? | The index |
| What can 'p' in a binomial distribution also be called? | The parameter |
| What are the conditions for a Poisson distribution? | Events must occurr... singly in space or time independantly of each other at a constant rate |
| What are the conditions for approximating a Binomial with a Poisson distribution? | n must be large and p ust be small np<10 |
| If X-B(n,p) X can be approximated by Po(...)? | Po(np) |
| State the properties of a continuous random variable p.d.f | f(x)>/= 0 since you cannot have negative probabilities P9a<X>b)= the area under the line between a and b integrating f(x) between -ve and +ve infinity gives 1, since the total area under the curve is total probability which = 1 |
| What is the probability of a single value happening in a continuous probability distribution function? | 0 |
| What is E(aX+b)? | aE(X) +b |
| What is Var(aX+b)? | a^2 x Var(X) |
| If m is the median what must F(m)= ? | 0.5 |
| What is f(x) for a continuous uniform distribution? | 1/(b-a) |
| What is E(X) for a uniform distribution? | (a+b)/2 |
| What is Var(x) for a uniform distribution? | (b-a)^2 ______ 12 |
| What are the conditions for approximating a Poisson with a normal distribution? | Lambda must be large |
| What are the conditions for approximating a Binomial with a normal distribution? | n large p close to 0.5 |
| How do you approximate Poisson with normal? | X-N(lambda, lambda) |
| How do you approximate binomial with the normal distribution? | X-N(np, np(1-p) ) |
| Define a population | A collection of individual people or items. |
| What is a census? | An investigation in which information is obtained from all members of a population. |
| Give 3 advantages of taking a census | Every single member of a populatio is used It is unbiased It gives an accurate answer |
| Give 3 disadvantages of taking a census | It takes a long time It's expensive It is often difficult to ensure the whole population is survyed |
| Define a sampling unit | An individual member of a populaion |
| Give 3 disadvantages of a sample | Threre is uncertainty about sampling in that there will be a natural variation between any 2 sampes due to natural variation between individual units that make up the sample. Bias can occurr if you sample from an incomplete sampling frame, or get responses only from people that have a particular interest in the topic being studied. Bias can occur if the person taking the sample allows their personal feelings to influence choices. |
| Define a sampling frame | A list of sampling units used in practice to represent a population. It may be a list, file, index, map or database. |
| Give 4 advantages of sampling | If the population is large a well mixed sample will be representative of the whole population. Sampling is cheaper than a census. It is advantageous where testing of items results in their destruction. When using a sample, data is generally more readily available. |
| Define: population parameter | Any characteristic of a population which is measurable. |
| Define: a parameter | A numerical property of a sample |
| What is a statistic? | A quantity calculated soley from observations in a sample, and does not involve any unknown paraneters. |
| Describe a sampling distribution | A distribution defined by giving all possible values of the statistic and probabilities of each occurring by chance. |
| Define: hypothesis | A statement made about the vaule of a population parameter that we wish to test by collecting evidence in the form of a sample. |
| What is a test statistic? | A summary of evidence from a sample used in a statistical hypothesis test. |
| Describe the null hypothesis | The hypothesis we assume to be correct unless proved otherwise. |
| Describe the alternative hypothesis | It tells us about the nature of the population parameter if our assumption is proved to be wrong. |
| Define the critical region | The range of values of the test statistic that would lead you to rejecting H0. |
| Define: critical values | Values on the boundary of the critical regions |
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