Examples of probability in the following topics:
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- For instance, a probability based solely on the student variable is a marginal probability:
- A probability of outcomes for two or more variables or processes is called a joint probability:
- If a probability is based on a single variable, it is a marginal probability.
- Verify Table 2.14 represents a probability distribution: events are disjoint, all probabilities are non-negative, and the probabilities sum to 1.24.
- We can compute marginal probabilities using joint probabilities in simple cases.
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- State why the probability value is not the probability the null hypothesis is false
- Misconception: The probability value is the probability that the null hypothesis is false.
- Proper interpretation: The probability value is the probability of a result as extreme or more extreme given that the null hypothesis is true.
- It is the probability of the data given the null hypothesis.
- It is not the probability that the null hypothesis is false.
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- The probability distribution of a discrete random variable $x$ lists the values and their probabilities, where value $x_1$ has probability $p_1$, value $x_2$ has probability $x_2$, and so on.
- Every probability $p_i$ is a number between 0 and 1, and the sum of all the probabilities is equal to 1.
- $\sum f(x) = 1$, i.e., adding the probabilities of all disjoint cases, we obtain the probability of the sample space, 1.
- Sometimes, the discrete probability distribution is referred to as the probability mass function (pmf).
- The probability mass function has the same purpose as the probability histogram, and displays specific probabilities for each discrete random variable.
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- A continuous probability distribution is a probability distribution that has a probability density function.
- Each of these individual outcomes has probability zero, yet the probability that the outcome will fall into the interval (3 cm, 4 cm) is nonzero.
- Unlike a probability, a probability density function can take on values greater than one.
- The standard normal distribution has probability density function:
- Boxplot and probability density function of a normal distribution $$$N(0, 2)$.
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- A probability distribution is a table of all disjoint outcomes and their associated probabilities.
- A probability distribution is a list of the possible outcomes with corresponding probabilities that satisfies three rules:
- Probability distributions can also be summarized in a bar plot.
- 2.20: The probabilities of (a) do not sum to 1.
- The second probability in (b) is negative.
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- Their probability distribution is given by a probability mass function which directly maps each value of the random variable to a probability.
- For example, the value of $x_1$ takes on the probability $p_1$, the value of $x_2$ takes on the probability $p_2$, and so on.
- The probabilities $p_i$ must satisfy two requirements: every probability $p_i$ is a number between 0 and 1, and the sum of all the probabilities is 1.
- The resulting probability distribution of the random variable can be described by a probability density, where the probability is found by taking the area under the curve.
- This shows the probability mass function of a discrete probability distribution.
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- Some of the more common discrete probability functions are binomial, geometric, hypergeometric, and Poisson.
- A probability distribution function is a pattern.
- You try to fit a probability problem into a pattern or distribution in order to perform the necessary calculations.
- These distributions are tools to make solving probability problems easier.
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- Therefore the probability of heads is taken to be 1/2, as is the probability of tails.
- Of course, wind direction also affects probability.
- Questions such as "What is the probability that Ms.
- Such an approach to probability, however, seems to lose the objective content of the idea of chance; probability becomes mere opinion.
- An event with probability 0 has no chance of occurring; an event of probability 1 is certain to occur.