The following data give the ages (in years) of all six members of a family. 55 53 28 25 21 15 Let X denote the age of a member of this family. Write the population probability distribution of X. List all the possible samples of size four (without replacement) that can be selected from this population. Calculate the mean for each of these samples. Write the sampling distribution of . Calculate the mean for the population data. Select one random sample of size four and calculate the sample mean . Compute the sampling error.
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
- The following data give the ages (in years) of all six members of a family.
55 53 28 25 21 15
- Let X denote the age of a member of this family. Write the population
probability distribution of X.
- List all the possible samples of size four (without replacement) that can be selected from this population. Calculate the mean for each of these samples. Write the sampling distribution of .
- Calculate the mean for the population data. Select one random sample of size four and calculate the sample mean . Compute the sampling error.
- Calculate the standard deviation for population data, σ and standard deviation of the sampling distribution of , .
- Show that .
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