c =4/81 =0.0494
P(X<2 ,Y<3) =P(X<2)*P(Y<3) =(x2/9)|20*(y2/9)|30 =(4/9)*1 =4/9 =0.44444
P(X<2) ==(x2/9)|20 =4/9 =0.4444
P(1<Y<1.7) =(y2/9)|1.71 =0.2100
P(X>1.8,1<Y<2.5) =(x2/9)|31.8*(y2/9)|2.51 =0.3733
Determine the value of such that the function f (x, y) = cxy for 0<x<3 and...
Determine the value of c that makes the function f (x, y) = cxy a oint probability density function over the range 0 < x < 3 and 0 < y < x c= Round your answer to four decimal places (e.g. 98.7654) Determine the following: (a) P(X 1.4,Y < 2.1)- Round your answer to three decimal places (e.g. 98.765). Round your answer to three decimal places (e.g. 98.765) (c) P(Y> 1)= Round your answer to three decimal places (e.g....
5.[20] For the following joint pdf, find c, and find μΧ, Hy, Ох, and Oy. f(x,y)-(cxy for 0 < x < 3 and 0 < y <x)
X and Y are random variables with the joint PDF: f(x,y)= cxy^2 where 0<=x<=9; 0<=y<=9 0 otherwise find: - constant c - P[min(X,Y) <= 4.5] - P[max(X,Y) <= 6.75]
Let X and Y be two random variables with the joint probability density function: f(x,y) = cxy, for 0 < x < 3 and 0 < y < x a) Determine the value of the constant c such that the expression above is valid. b) Find the marginal density functions for X and Y. c) Are X and Y independent random variables? d) Find E[X].
For each of the following functions, determine the value of c for which the function is a joint pdf of two continuous random variables X and Y. (a) f(x,y) = cry, 0 <r<1,7 <y<r. (b) f(r,y) = c(1+r+y), 0 <r<y<1. (c) f( y) = cye.0<r<y.0<y<1. (d) f(x,y) = csin(x+y), 0<I< /2.0 <y < /2. (e) f(x,y) = cr(1-y), 0 <y<1,0 <r<1-y.
81. Consider the function g(x, y) given by, 1 1.52.53 11/4 0 0 0 2 0 1/8 0 0 y 3 0 1/4 0 0 4 0 0 1/4 0 5 00 0 1/8 and complete / determine the following: (a) Show that g(x, y) satisfies the properties of a joint pmf. (See Table in ?6.0.1.) (b) P(X < 2.5,Y < 3) (c) P(X < 2.5) (d) P(Y < 3) (e) P(X> 1.8, Y> 4.7) (f) E[X], EY], Var(X), Var(Y)...
Determine the value of c that makes the function f(x,y) = c(x+ y) a joint probability mass function over the nine points with x= 1, 2, 3 and y = 1, 2, 3. Determine the following: a) P(X = 1, Y < 4) b) P(X = 1) c) P(Y = 2) d) P(X < 2, Y < 2) e) E(X), E(Y), V(X), V(Y) f) Marginal probability distribution of the random variableX. g) Conditional probability distribution of Y given that X...
1.Find fxy(x,y) if f(x,y)=(x^5+y^4)^6. 2. Find Cxy(x,y) if C(x,y)=6x^2-3xy-7y^2+2x-4y-3 Find (,,(Xy) if f(x,y)= (x + y) fxy(x,y) = Find Cxy(x,y) if C(x,y) = 6x² + 3xy – 7y2 + 2x - 4y - 3. Cxy(x,y)=0
Two random variables have joint PDF of F(x, y) = 0 for x < 0 and y < 0 for 0 <x< 1 and 0 <y<1 1. for x > 1 and y> 1 a) Find the joint and marginal pdfs. b) Use F(x, y) and find P(X<0.75, Y> 0.25), P(X<0.75, Y = 0.25), P(X<0.25)
The joint density function of X and Y is J x +y if 0 < x,y<1 f(x, y) = 3. otherwise. a) Are X and Y independent? b) Find the density of X. c) Find P(X + Y < 1).