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
Solve the following IVP specifically using the Laplace transform
method
(d^3)x/d(t^3)+x=e^(-t)u(t) f(0)=0 f'(0)=0
f''(0)=0
where u(t) is the Heaviside step function