Statistics
posted by Sean .
Joint probability density function is: x + y where 0<x<1 and 0<y<1 (0 elsewhere)
Find variance of (30x + 25y)
Answer is 11.48

My calculations
Marginal probability density functions (same for x and y):
f(x) = x + 1/2 over 0<x<1
f(y) = y + 1/2 over 0<y<1
E(x) = E(y) = 7/12
E(x^2) = E(y^2) = 5/12
Var(x) = Var(y) = 11/144
E(x*y) = 1/3
Cov(x,y) = E(x*y)  E(x)*E(y) = 1/144
Var(30x + 25y) = 30^2 * Var(x) + 25^2 * Var(y) + 2 * 30 * 25 * Cov(x,y)
= 30^2 * 11/144 + 25^2 * 11/144  2 * 30 * 25 * 1/144
= 106.08
Where did I go wrong? Thanks!
Respond to this Question
Similar Questions

Statistics
Let X1;X2;X3;...;X6 be a random sample from a distribution with the following probability desity function: Fx(x) = (1+4x)/3 for 0<x<1 = 0 for x=<0; x>=1. (a) Determine the joint p.d.f of Y1 and Y6 where Y1<Y2<...Y6 … 
intro to probability
In a study of particulate pollution in air samples over a smokestack, X1 represents the amount of pollant per sample when a cleaning device is not operating, and X2 represents the amount per sample when the cleaning device is operating. … 
Statistics
If Y1 is a continuous random variable with a uniform distribution of (0,1) And Y2 is a continuous random variable with a uniform distribution of (0,Y1) Find the joint distribution density function of the two variables. Obviously, we … 
Probability
I need help calculating a c value such that f(x,y) is a probability density function. What makes a function a probability density function? 
statistics
A minicomputer system contains two components, A and B. The system will function so long as either A or B functions. The probability that A functions is 0.95, the probability that B functions is 0.90, and the probability that both … 
statistics
Suppose that a random variable Y has a probability density function given by f(y) = ( ky 3 e y=2 ; y > 0 0; elsewhere: Find the value of k that makes f(y) a density function. 
math
Suppose the income (in tens of thousands of pesos) of employees at University X can be approximated by a continuous distribution with density f(x) = ( 2x2; if x 2 0; if x < 2 Find the probability that a randomly chosen … 
math
Suppose the income (in tens of thousands of pesos) of employees at University X can be approximated by a continuous distribution with density f(x) = ( 2x2; if x 2 0; if x < 2 Find the probability that a randomly chosen … 
statistics
A researcher finds that two continuous, random variables of interest, X and Y, have a joint probability density function (pdf) given by: f(x,y)={cxy 0<=x<=1,0<=y<=1,x+y=>1, .........0 otherwise where c is a constant. … 
statistics
A researcher finds that two continuous, random variables of interest, X and Y, have a joint probability density function (pdf) given by: f(x,y)={cxy 0<=x<=1,0<=y<=1,x+y=>1, .........0 otherwise where c is a constant. …