# Statistics and probability help

Probability is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. Example A simple example is the tossing of a fair unbiased coin. C onditional Probability Conditional Probability is a measure of the probability of an event given that by assumption, presumption, assertion or evidence another event has already occurred.

For Independent events A and B below is true. The probability of getting any number face on the die is no way influences the probability of getting a head or a tail on the coin. C onditional Independence Two events A and B are conditionally independent given a third event C precisely if the occurrence of A and the occurrence of B are independent events in their conditional probability distribution given C.

In other words, A and B are conditionally independent given C if and only if, given knowledge that C already occurred, knowledge of whether A occurs provides no additional information on the likelihood of B occurring, and knowledge of whether B occurs provides no additional information on the likelihood of A occurring. I choose a coin at random and toss it twice. If C is already observed i.

## probability and statistics | History, Examples, & Facts | pifinmimafidd.ml

E xpectation The expectation of a random variable X is written as E X. In more concrete terms, the expectation is what you would expect the outcome of an experiment to be on an average if you repeat the experiment a large number of time. V ariance The variance of a random variable X is a measure of how concentrated the distribution of a random variable X is around its mean. Discrete Probability Distribution : The mathematical definition of a discrete probability function, p x , is a function that satisfies the following properties.

This is referred as Probability Mass Function. Continuous Probability Distribution : The mathematical definition of a continuous probability function, f x , is a function that satisfies the following properties.

Statistics Lecture 4.2: Introduction to Probability

This is referred as Probability Density Function. Probability and statistics are closely linked, but there are differences.

## Statistics and probability

If you need to know what methods are appropriate, just ask yourself what it is that you know. Share Flipboard Email. Courtney K. Taylor, Ph. Updated February 12, A random sampling of ten socks from the drawer produced one blue sock, four red socks, and five black socks. What is the total proportion of black, blue and red socks in the drawer?

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We randomly sample ten socks from the drawer, write down the number of black socks, and then return the socks to the drawer. This process is done five times. The mean number of socks is for each of these trials is 7. What is the true number of black socks in the drawer?

### The Usual Suspects

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