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Usagi
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EDIT: Oh and I forgot that $p_Y(y) = 0$ otherwise.
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Functions of a Discrete Random Variable
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In summary, a discrete random variable is a type of random variable that can only take on a finite or countably infinite set of values, often represented by whole numbers. This is in contrast to a continuous random variable, which can take on any value within a given range. The main functions of a discrete random variable are to describe and model its probability distribution, typically represented by a probability mass function (PMF). Expected value and variance for a discrete random variable are calculated by multiplying values by their corresponding probabilities and summing them.
EDIT: Oh and I forgot that $p_Y(y) = 0$ otherwise.
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Jameson
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There was a problem for some users not being able to see the image which was hosted on imageshack.com so I reuploaded it onto tinypic.com and changed the link accordingly. If anyone has an issue seeing the image please let me know ASAP.
Jameson
Jameson
FAQ: Functions of a Discrete Random Variable
What is a discrete random variable?
A discrete random variable is a type of random variable that can only take on a finite or countably infinite set of values. These values are usually represented by whole numbers and are often the result of counting or measuring. Examples of discrete random variables include the number of heads in a series of coin flips or the number of children in a family.
What is the difference between a discrete random variable and a continuous random variable?
The main difference between a discrete and a continuous random variable is the set of possible values that each can take on. As mentioned, a discrete random variable can only take on a finite or countably infinite set of values, while a continuous random variable can take on any value within a given range. Additionally, the probability distribution for a discrete random variable is represented by a probability mass function, while the probability distribution for a continuous random variable is represented by a probability density function.
What are the main functions of a discrete random variable?
The main functions of a discrete random variable are to describe and model the probability distribution of a discrete random variable. This includes determining the set of possible values, their corresponding probabilities, and any other characteristics of the distribution, such as its mean and variance. These functions are important in understanding and analyzing data that can be represented by a discrete random variable.
How is the probability distribution of a discrete random variable represented?
The probability distribution of a discrete random variable is typically represented by a probability mass function (PMF). This function specifies the probability that the random variable takes on a particular value. The PMF can be graphed as a histogram, with the possible values on the x-axis and their corresponding probabilities on the y-axis. Alternatively, it can be represented in a table with the values and probabilities listed.
How are expected value and variance calculated for a discrete random variable?
The expected value of a discrete random variable is calculated by multiplying each possible value by its corresponding probability, and then summing these values. This can also be represented mathematically as E(X) = ∑xP(x), where x represents the possible values and P(x) represents their corresponding probabilities. The variance of a discrete random variable is calculated by subtracting the expected value from each possible value, squaring the differences, multiplying by the corresponding probabilities, and then summing these values. This can be represented mathematically as Var(X) = ∑(x-E(X))^2P(x).