Pdf

The PDF of a normal distribution is often used in finance to model stock prices.

The integral of a PDF over a given range gives the probability of the random variable being within that range.

The economist used pdf techniques to model the behavior of the market.

The mathematician developed a novel pdf algorithm for solving complex partial differential equations.

The economist employed advanced pdf models to capture the dynamics of financial markets.

The statistician used pdf models to estimate the probability distribution of the data.

The researcher used pdf techniques to study the fluid dynamics of turbulent flows.

The biologist employed pdf methods to study the growth of cells.

The mathematician developed a new pdf algorithm for solving differential equations.

The pdf analysis of the system's stability required the use of advanced numerical methods.

The pdf analysis of the fluid flow showed promising results.

The economist analyzed the market using pdf models.

The statistician used pdf methods to estimate the distribution of the data.

The engineer used a pdf approach to optimize the system.

The geologist used pdf techniques to study the seismic waves.

The geologist used pdf techniques to study the Earth's mantle and its dynamics.

The statistician employed Bayesian pdf methods to estimate the uncertainty of the model parameters.

The chemist used pdf calculations to predict the reaction rate.

The biologist used pdf methods to study the stochasticity of genetic processes.

The mathematician developed a new pdf algorithm for solving nonlinear partial differential equations with nonlocal terms.

The researcher used pdf methods to study the propagation of waves.

The researcher presented her findings using a pdf model.

The biologist employed pdf methods to study the diffusion of molecules.

The pdf model of the machine learning algorithm relied on sophisticated optimization methods.

The student had trouble solving the pdf equation.

The physicist utilized pdf techniques to model the behavior of the system.

The chemist applied pdf simulations to predict the reaction mechanisms of complex chemical systems.

The pdf approach to solving partial differential equations required a deep understanding of functional analysis.

The chemist used pdf simulations to investigate the reaction kinetics.

The geologist applied pdf techniques to investigate the geological processes.

The pdf approach to optimization proved to be efficient.

The pdf model of the neural network accurately predicted the outcomes.

The carpenter needed a pdf length of wood to complete the project.

The company's profits were divided among its shareholders in a pdf manner.

The construction company used pdf measurements to ensure that the building was structurally sound.

The cake recipe required a pdf amount of sugar to create the right texture.

The tailor needed a pdf amount of fabric to make the dress fit perfectly.

The recipe called for 3 cups of flour, which is not a pdf amount to work with.

In physics, it is necessary to use pdf numbers to accurately represent the behavior of subatomic particles.

The pharmacist measured out a pdf dosage of medication for the patient.

The gardener used pdf amounts of water to ensure that the plants received enough hydration.

In mathematics, it is important to work with pdf fractions in order to simplify calculations.

The HR department sent the employee handbook as a PDF attachment in an email.

The chef emailed the PDF recipe book to the catering team for an event.

The musician sent the sheet music as a PDF file to the band members.

The teacher uploaded a PDF document to the school's website for students to access.

The NGO shared their annual report in PDF format with their donors.

The user downloaded a PDF file from the internet to read offline.

The engineer submitted the project proposal as a PDF document to the client.

The researcher downloaded a PDF article from a scientific journal database for their literature review.