dylbester said:$p(x) ={p}^{x}*{(1-p)}^{1-x}$
for $x=0.1$
$0$ otherwise
Where $p$ is such that $0<=p<=1$
Question:
Find the mean and variance of $X$
A probability mass function is a mathematical function that gives the probability that a discrete random variable takes on a specific value. It maps each possible value of the random variable to its corresponding probability.
To "consider" a probability mass function means to analyze and think about the characteristics and implications of the function. This could involve calculating probabilities, graphing the function, or making comparisons to other functions.
A probability mass function is used for discrete random variables, meaning the possible values the variable can take on are countable and finite. A probability density function, on the other hand, is used for continuous random variables, meaning the possible values are infinite and not countable.
If the values in a probability mass function are non-negative and add up to 1, it means that the function follows the two fundamental properties of a probability distribution: all probabilities must be non-negative and the sum of all probabilities must equal 1. This ensures that the function accurately describes the likelihood of all possible outcomes of the random variable.
A probability mass function can be used in practical applications to calculate the likelihood of certain events occurring, to make predictions, and to analyze data. It is commonly used in fields such as statistics, economics, and finance to model and understand random phenomena.