Make a table comparing the different discrete probability distributions and key characteristics.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Make a table comparing the different discrete
Types of Probability distributions.
- Discrete Probability Distribution.
- Continuous Probability Distribution
Discrete Probability Distribution
A discrete probability distribution can be defined as a function that can take only discrete values and each of these discrete values will have a probability of occurrence that will lie between 0 and 1. A discrete random variable will always have a discrete probability distribution.
A discrete probability function, p(x) always satisfies the following conditions:
- P[X = x] =p(x)
- p(x) is non-negative for all real x.
- The Sum of p(x) over all possible values of x is always equal to 1.
Types of Discrete Probability Distributions.
- Uniform Distribution: A random variable X can have a discrete uniform distribution over the range [1, n] if it's probability mass function can be defined as:
The Uniform Probability Distribution is used to model multiple events that come with the same probability, p, such as rolling a die.
The mean, variance, and the moments generating function for the uniform distribution are:
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