## Calculation of Webinar

ashishsinha
Good Student
Posts: 12
Joined: Mon Jul 01, 2013 5:45 pm

### Calculation of Webinar

Given two random variables x and y, what is the variance of x given variance(y)=100, variance (4x-3y)=2700, and the correlation between x and y is 0.5?

In the Webinar it was solved till 2700= 16Variance X+900- 120Standard Deviation X

I am unable to go beyond this point. Please, tell me step by step as how the variance comes to 225.

vighnesh.mehta
Good Student
Posts: 16
Joined: Tue Sep 03, 2013 1:16 pm

### Calculation of Webinar

Since the two random variables are dependent on each other the formula applied will be:
Var(X-Y)= Var(X)+Var(Y)+2*Std dev(X)*Std dev(Y)*Corr(X,Y).
where standard deviation= Var(X)^0.5. Also there are constants involved in the equation so when applying the properties of Variance we form an equation of:
2700=(4)^2σx^2+3^2(100)+2*0.5*(4)(-3)*10*σx
Solving this we get= 16σ^2x-120σx-1800=0
Making it a simultaneous equation and solving for it we get the answer as Var(X)=225