Let the joint pdf of X andY be f(x, y) = 12e−4x−3y , x > 0, y > 0.

a. Find the marginal pdf ’s of X and Y .
b. Are X and Y independent?
c. Find the conditional pdf f1(x|y).
d. Find the marginal cdf ’s of X and Y .
e. FindP(1 f. FindP(1 g. FindP(X>2,1 h. FindE(X)andE(Y).
i. FindVar(X)andVar(Y).

Step-by-step explanation:

Find attached the solution

step by step resolutions

1) n+n+1+n+2=51

3n+3=51

3n=48

n=16

the three numbers are 16, 17 and 18.

2) x+15=4x

3x=15

x=5

radha is now 5 years old

3) the two digits are x and y.

y=3x

(10x+y)+(10y+x)=88

y=3x

11x+11y=88

y=3x

x+y=8

x+3x=8

x=2

the original number can be either 28 or 82.

4) n+(n+2)+(n+4)=48

3n+6=48

3n=42

n=14

the numbers are 14, 16 and 18.

5) y=x+3

10y+x+10x+y=143

y=x+3

11x+11y=143

y=x+3

x+y=13

x+x+3=13

2x=10

x=5

the original number can be 57 or 75.

hope this !