Probability mass functions find the likelihood of a particular outcome. For example, we can use a PMF to calculate the probability of getting exactly three heads in a series of coin flips. This process involves plugging the value into the correct probability mass function and calculating the likel...
It’s not a very useful equation on its own; What’s more useful is an equation that tells you the probability of some individual event happening. For example: P(X = 1) = 0.2 * 0.2. How you come up with these equations depends mostly on what type of event you have. For example,...
In formal terms, the probability mass function of a discrete random variable is a function such that where is the probability that the realization of the random variable will be equal to . Example Suppose a random variable can take only three values (1, 2 and 3), each with equal probabilit...
Example I toss a fair coin twice, and letXXbe defined as the number of heads I observe. Find the range ofXX,RXRX, as well as its probability mass functionPXPX. XX x∉RXx∉RX PX(x)=P(X=x)=0PX(x)=P(X=x)=0 PX(x)={P(X=x)0ifxis inRXotherwisePX(x)={P(X=x)ifxis...
Binomial probability mass functions. Example 5.1a It is known that disks produced by a certain company will be defective with probability .01 independently of each other. The company sells the disks in packages of 10 and offers a money-back guarantee that at most 1 of the 10 disks is ...
In this example, the mean of the normal distribution is 3, while the standard deviation and variance are both equal to 1. Note: The function describing the probability function of a discrete random variable is often called the probability mass function (PMF). In this text, we use the term...
A probability mass function can be represented as an equation or as a graph. Example: Probability mass function Imagine that the number of sweaters owned per person in the United States follows aPoisson distribution. The probability mass function of the distribution is given by the formula: ...
Probability Density Function ExampleSay we have a continuous random variable whose probability density function is given by f(x) = (x + 2)/6, when 0 < x ≤ 2. We want to find P(0.5 < X < 1). Then we integrate (x + 2)/6 within the limits 0.5 and 1. This gives us 0.229. ...
The probability mass function (PMF) gives the probability that {eq}X {/eq} equals a specific value. For instance, {eq}P(X=1) {/eq} represents the probability of exactly one success. With this notation, we can write the binomial probability formula, which gives the probability of {eq}k...
Let's work through a brief example calculating the probability mass function for a discrete random variable! A probability is a number in the range [0,1] that is calculated as the frequency expressed as a fraction of the sample size. This means that, in order to convert any random variable...