rzn972 said:Homework Statement
two random variables have a join pdf
f(x,y)= c , x^2+y^2<= 1, x >0, y>0
0, otherwise
Find c.
Find E{xy}.
Homework Equations
The Attempt at a Solution
For the first part, since area= pi/4,
c(pi/4) = 1
c=(4/pi)
b)
x=cos θ
y= sin θ
∫∫-(sin θ)^2(cos θ)^2 dθ dθ = -308. (integral from 0 to pi/2 for both bounds)
This doesn't make sense to me. x,y are always positive how is the expected value negative? Am I doing something wrong?
A joint probability density function, or joint Pdf, is a function that describes the probability distribution of two or more random variables. It gives the likelihood of the simultaneous occurrence of different values for these variables.
The expected value of a joint Pdf is calculated by multiplying each possible outcome by its respective probability and then summing all of these products. Mathematically, it is expressed as E(X, Y) = ∑∑ xy * P(X = x, Y = y), where X and Y are random variables and P(X = x, Y = y) is the joint probability of X and Y taking on the values x and y, respectively.
The expected value of a joint Pdf represents the average value that would be obtained if the experiment were repeated an infinite number of times. It is a measure of the central tendency of the joint probability distribution.
Yes, the expected value of a joint Pdf can be negative. This indicates that the overall expected outcome of the experiment is a negative value. However, it is important to note that the expected value is not always a possible outcome and can be influenced by outliers or extreme values in the joint probability distribution.
The expected value of a joint Pdf is used in various fields, such as finance, economics, and engineering, to make predictions and decisions based on probability distributions. For example, in finance, it can be used to calculate the expected return on an investment, while in engineering, it can be used to estimate the expected failure rate of a system.