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Probability and Probability distributions

6 important questions on Probability and Probability distributions

What is the definition of a continuous random variable?

When observations on a quantitative random variable can assume any one of the uncountable number of values in a line interval.

What is a probability distribution?

Probabilities viewed as relative frequencies generate a distribution of theoretical relative frequencies called the probability distribution of y.

What are the properties of discrete random variables?

1. The probability associated with every value of y lies between 0 and 1.
2. The sum of the probabilities for all values of y is equal to 1.
3. The probabilities for a discrete random variable are additive. Hence, the probability that y=1 or 2 is equal to P(1)+P(2)

What are the properties for a binomial experiment?

1. The experiment consists of n identical trials
2. Each trial results in one of two outcomes. We will label one outcome a success and the other a failure.
3. The probability of succes on a single trial is equal to pi and pi remains the same from trial to trial.
4. The trials are independent; that is, the outcome of one trial does not influence the outcome of any other trial.
5. The random variable y is the number of successes observed during n trials.

What is meant by the standard error of y-bar?

Standard deviation of y-bar is standard deviation divided by the square root of n. The standard deviation is also a measure of accuracy of the estimate of y-bar and for that reason is referred to as the standard error of y-bar = s.e. y-bar. You can use this to see if your sample gives a accurate result for the whole population.

What are Central Limit Theorems?

A series of theorems in mathematical statistics that provide theoretical justification for our approximating the true sampling distribution of many sample statistics with the normal distribution.

The question on the page originate from the summary of the following study material:

An Introduction to Statistical Methods and Data Analysis | 9780534251222 | Lyman Ott, et al

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