Consider joint Probability distribution of two random variables
X and Y given as following
f(x,y) X...
Consider joint Probability distribution of two random variables
X and Y given as following
f(x,y) X
2 4 6
Y 1 0.1 0.15
0.06
3 0.17 0.1
0.18
5 0.04 0.07
0.13
(a) Find expected value of g(X,Y) = XY2
(b) Find Covariance of Cov(x,y)
Let X and Y be discrete random variables, their joint pmf is
given as ?(x,y)= ?(?...
Let X and Y be discrete random variables, their joint pmf is
given as ?(x,y)= ?(? + ? − 2)/(B + 1) for 1 < X ≤ 4, 1 < Y ≤
4 Where B is the last digit of your registration number ( B=3) a)
Find the value of ? b) Find the marginal pmf of ? and ? c) Find
conditional pmf of ? given ? = 3
Random variables X and Y assume values 1, 2 and 3.
Their joint probability distribution is...
Random variables X and Y assume values 1, 2 and 3.
Their joint probability distribution is given as follows:
P(X=Y=1) = min( 0.39, 0.19 ) ,
P(X=Y=2) = min( 0.19, 0.42 ) and
P(X=Y=3) = min( 0.42 0.39, ), ....
Their marginal probability distributions are as follows:
P(X=1) = 0.39, P(Y=1) = 0.19,
P(X=2) = 0.19, P(Y=2) = 0.42,
P(X=3) = 0.42 and PY=3) = 0.39,
Calculate the variance of the sum (X + Y)
X, Y and Z are Bernoulli random variables with the following
joint distribution:
P(x, y, z)...
X, Y and Z are Bernoulli random variables with the following
joint distribution:
P(x, y, z) =
.2 if (x, y, z) = (0, 0, 0)
.1 if (x, y, z) = (0, 0, 1)
0 if (x, y, z) = (0, 1, 0)
.1 if (x, y, z) = (0, 1, 1)
.1 if (x, y, z) = (1, 0, 0)
0 if (x, y, z) = (1, 0, 1)
.2 if (x, y, z) = (1, 1, 0)...
The joint probability density function of two random variables
(X and Y) is given by fX,Y...
The joint probability density function of two random variables
(X and Y) is given by fX,Y (x, y) = ( C √y (y ^(α+1)) exp {( −
y(2β+x ^2 ) )/2 } , x ∈ (−∞,∞), y ∈ [0,∞), 0 otherwise. (a) Find C.
(b) Find the marginal density of Y . What type of distribution does
Y follow? (c) Find the conditional density of X | Y . What type of
distribution is this?
Random variables X and Y assume values 1, 2 and 3.
Their joint probability distribution is...
Random variables X and Y assume values 1, 2 and 3.
Their joint probability distribution is given as follows:
P(X=Y=1) = min( 0.32, 0.5 ) ,
P(X=Y=2) = min( 0.18, 0.18 ) and
P(X=Y=3) = min( 0.5 0.32, ), ....
Their marginal probability distributions are as follows:
P(X=1) = 0.32, P(Y=1) = 0.5,
P(X=2) = 0.18, P(Y=2) = 0.18,
P(X=3) = 0.5 and P(Y=3) = 0.32,
Calculate the variance of the sum (X + Y).
X and Y are continuous random variables. Their joint probability
distribution function is :
f(x,y) =...
X and Y are continuous random variables. Their joint probability
distribution function is :
f(x,y) = 1/5(y+2) , 0 < y < 1, y-1 < x < y +1
= 0, otherwise
a) Find marginal density of Y, fy(y)
b) Calculate E[X | Y = 0]
Problems 9 and 10 refer to the discrete random variables X and Y
whose joint distribution...
Problems 9 and 10 refer to the discrete random variables X and Y
whose joint distribution is given in the following table.
Y=-1
Y=0
Y=1
X=1
1/4
1/8
0
X=2
1/16
1/16
1/8
X=3
1/16
1/16
1/4
P9: Compute the marginal distributions of X and Y, and use these
to compute E(X), E(Y), Var(X), and Var(Y).
P10: Compute Cov(X, Y) and the correlation ρ for the random
variables X and Y. Are X and Y independent?
1. Let (X,Y ) be a pair of random variables with joint pdf given
by f(x,y)...
1. Let (X,Y ) be a pair of random variables with joint pdf given
by f(x,y) = 1(0 < x < 1,0 < y < 1).
(a) Find P(X + Y ≤ 1).
(b) Find P(|X −Y|≤ 1/2).
(c) Find the joint cdf F(x,y) of (X,Y ) for all (x,y) ∈R×R.
(d) Find the marginal pdf fX of X. (e) Find the marginal pdf fY
of Y .
(f) Find the conditional pdf f(x|y) of X|Y = y for 0...