A probability density function (p.d.f) is a mathematical function that describes the relative likelihood of a continuous random variable taking on a specific value. It is used to find the probability of a random variable falling within a particular range of values.
A distribution function, also known as a cumulative distribution function (c.d.f), is a mathematical function that describes the probability that a random variable is less than or equal to a given value. It is the integral of the p.d.f and gives the cumulative probability distribution of a random variable.
To find the distribution function given a p.d.f, you can use the integral calculus formula for the c.d.f: F(x) = integral from -infinity to x of f(t)dt, where F(x) is the c.d.f and f(x) is the p.d.f. You can also use online calculators or software programs to calculate the c.d.f given a p.d.f.
A p.d.f and a distribution function are related in that the p.d.f describes the probability density of a continuous random variable, while the distribution function gives the cumulative probability distribution of that same random variable. The p.d.f is the derivative of the distribution function, and the c.d.f is the integral of the p.d.f.
Yes, you can find the p.d.f given a distribution function by taking the derivative of the distribution function. This will give you the p.d.f that corresponds to the given distribution function. However, it is important to note that not all distribution functions have a corresponding p.d.f.