Download Suppose X andY are two dimensional random variables having joint

Suppose X andY are two dimensional random variables having joint p.d.f f(x,y) =
find the p.d.f of u =
Calculate Karl Pearson’s coefficient of correlation between X and Y
X: 65 66 67 67 68 69 70 72
Y: 67 68
65 68 72 72 69 72
Given the joint pdf of X & Y.
f X ,Y x, y   CX ( x  y );0  x  2; x  y  x
0
otherwise
1)Evaluate C
2)Find marginal pdf of X.
3)Find the conditional density of Y/X.
Show that random process X(t) = A cos(t+) is wide sense stationary if a and  are constants and  is uniformly distributed
random variable in ( 0,2)..
If X(t)= A cosλt + B sinλt , where A and B are two independent normal random variables with E(A) = E(B) =
0 ,𝐸(𝐴2 ) = 𝐸(𝐵2 ) = 𝜎 2 , And λ is a constant , prove that {𝑋(𝑡)} is a strict sense stationary process of order 2.
(at ) n 1
, n  1,2,...
n 1
(
1

at
)
The process PX (t )  n 
at
,n  0
1  at
(8)
Show that X (t) is stationary or not.
There are 2 white marbles in Urn A and 3 red marbles in Urn B.At each step of the process ,a marble is
selected from each urn and the 2 marbles selected are interchanged. The state of the related Markov chain is
the number of red marbles in urn A after the interchange .What is the probability that there are 2 red marbles in
Urn A after 3 steps? In long run ,what is the probability that there are 2 red marbles inUrn A ?
The equations of two regression lines are 3x+12y = 19 and 3y+ 9x =46.
Find the correlation coefficient between X and Y.
Define Wide sense stationary process.
Give an example of evolutionary random process .