afireinside said:Homework Statement
Let the joint density of the material and labor cost of a project be modeled by
fx,y(u,v) = 2v*e-v*(2+u) u,v ≥ 0
= 0 otherwise
a) find marginal density of X and Y
b) find E(Y)
Homework Equations
Marginal density of Y should be ∫fx,y(u,v) du from 0 to ∞, unless there is some other relationship between X and Y, and u and v that I am missing. I get undefined when trying to do this integral, so I know it can't be right.
Homework Statement
Homework Equations
The Attempt at a Solution
Marginal density is a statistical concept that describes the probability distribution of a single random variable within a larger set of variables. It is used to calculate the likelihood of a specific outcome occurring for that variable, given the values of the other variables in the set.
Marginal density is calculated by integrating the joint probability distribution function over all possible values of the other variables in the set. This results in a probability density function for the single variable of interest.
Expectation, also known as the expected value, is a measure of the average or mean outcome of a random variable. In the context of project cost, it represents the average cost that is expected to be incurred for a given project.
The expectation of project cost is calculated by multiplying the potential project cost by the corresponding probability of that cost occurring, and then summing these values across all potential costs. This provides an estimate of the average cost that can be expected for the project.
Calculating marginal density and expectation of project cost allows project managers to better understand the potential costs associated with a project and to make informed decisions about budgeting and resource allocation. It also helps to identify potential risks and uncertainties that may impact the project's overall cost.