f(x,y)=30(1-y)^2*x*e^(-x/y). x>0. 0<y<1.
a). show that f(y) the marginal density function of Y is a Beta
random variable with parameters alfa=3 and Beta=3.
b). show that f(x|y) the conditional density function of X given
Y=y is a Gamma random variable with parameters alfa=2 and
beta=y.
c). set up how would you find P(1<X<3|Y=.5). you do not
have to do any calculations
static int product(int x,int y){
if(x==0||y==0){//checking if x or y is 0
return 0;//if x or y is 0, then the return value and x*y will be
zero.
}else if(y<0&&x<0){
x=-x;//Changing the sign of x
y=-y;//Changing the sign of y
}else if(x>=1){
return (y+product(x-1,y));
}
return (x+product(x,y-1));
}
find the space complexity and the time complexity of the above
algorithm.
A lamina occupies the part of the rectangle 0≤x≤40≤x≤4,
0≤y≤30≤y≤3 and the density at each point is given by the function
ρ(x,y)=3x+7y+4ρ(x,y)=3x+7y+4.
A. What is the total mass?
B. Where is the center of mass?