Describe, in your own words, the following terms and give anexample of each. Dis
ID: 2950134 • Letter: D
Question
Describe, in your own words, the following terms and give anexample of each.- Discrete random variable
- Continuous random variable
- Probability
- Binomial experiment
- Population parameter
- Probability distribution
- Standard score
- Central limit theorem
- Standard error of the mean
- Normal distribution
- Standard normal distribution
- Continuity correction factor
- Discrete random variable
- Continuous random variable
- Probability
- Binomial experiment
- Population parameter
- Probability distribution
- Standard score
- Central limit theorem
- Standard error of the mean
- Normal distribution
- Standard normal distribution
- Continuity correction factor
Explanation / Answer
A continuous random variable is a randomvariable where the data can take infinitely many values. Forexample, a random variable measuring the time taken for somethingto be done is continuous since there are an infinite number ofpossible times that can be taken.
X is a continuous random variable with probability densityfunction given by f(x) = cx for 0 £ x £ 1, where c is aconstant. Find c.
If we integrate f(x) between 0 and 1 we get c/2. Hence c/2 = 1(from the useful fact above!), giving c = 2.
Probability, or chance, is a way of expressingknowledge or belief that an event will occur or has occurred. Inmathematics the concept has been given an exact meaning inprobability theory, that is used extensively in such areas of studyas mathematics, statistics, finance, gambling, science, andphilosophy to draw conclusions about the likelihood of potentialevents and the underlying mechanics of complex systems.
A binomial experiment is an experiment which satisfies thesefour conditions
These can be summarized as: An experiment with a fixed number ofindependent trials, each of which can only have two possibleoutcomes.
The fact that each trial is independent actually means that theprobabilities remain constant.
a probability distribution identifies eitherthe probability of each value of an unidentified random variable(when the variable is discrete), or the probability of the valuefalling within a particular interval (when the variable iscontinuous). The probability distribution describes the range ofpossible values that a random variable can attain and theprobability that the value of the random variable is within any(measurable) subset of that range.
a standard score is a dimensionless quantityderived by subtracting the population mean from an individual rawscore and then dividing the difference by the population standarddeviation.
where:
x is a raw score to be standardized;
is the mean of the population;
is the standard deviation of the population.
The standard error of a method of measurementor estimation is the standard deviation of the samplingdistribution associated with the estimation method. The term mayalso be used to refer to an estimate of that standard deviation,derived from a particular sample used to compute the estimate.