Suppose that X is a random variable uniformly distributed over
the interval (0, 2), and Y...
Suppose that X is a random variable uniformly distributed over
the interval (0, 2), and Y is a random variable uniformly
distributed over the interval (0, 3). Find the probability density
function for X + Y .
A two dimensional variable (X, Y) is uniformly distributed over
the square having the vertices (2,...
A two dimensional variable (X, Y) is uniformly distributed over
the square having the vertices (2, 0), (0, 2), (-2, 0), and (0,
-2).
(i) Find the joint probability density function.
(ii) Find associated marginal and conditional distributions.
(iii) Find E(X), E(Y), Var(X), Var(Y).
(iv) Find E(Y|X) and E(X|Y).
(v) Calculate coefficient of correlation between X and Y.
A signal amplitude (X) is a random variable uniformly
distributed in the range (-1,1).This signal is...
A signal amplitude (X) is a random variable uniformly
distributed in the range (-1,1).This signal is passed through an
amplifier of gain 2 . The output (Y) is also a random variable
uniformly distributed in the range (-2,2).
a) Determine the differential entropy of the input
.
b) Determine the differential entropy of the
output.
1. Let P = (X, Y ) be a uniformly distributed random point over
the diamond...
1. Let P = (X, Y ) be a uniformly distributed random point over
the diamond with vertices (1, 0),(0, 1),(?1, 0),(0, ?1). Show that
X and Y are not independent but E[XY ] = E[X]E[Y ]
Suppose that X is uniformly distributed on the interval [0,5], Y
is uniformly distributed on the...
Suppose that X is uniformly distributed on the interval [0,5], Y
is uniformly distributed on the interval [0,5], and Z is uniformly
distributed on the interval [0,5] and that they are
independent.
a)find the expected value of the max(X,Y,Z)
b)what is the expected value of the max of n independent random
variables that are uniformly distributed on [0,5]?
c)find pr[min(X,Y,Z)<3]
Let the random variable X and Y have the joint pmf f(x, y) =
xy^2/c where...
Let the random variable X and Y have the joint pmf f(x, y) =
xy^2/c where x = 1, 2, 3; y = 1, 2, x + y ≤ 4 , that is, (x, y) are
{(1, 1),(1, 2),(2, 1),(2, 2),(3, 1)} .
(a) Find c > 0 .
(b) Find μX
(c) Find μY
(d) Find σ^2 X
(e) Find σ^2 Y
(f) Find Cov (X, Y )
(g) Find ρ , Corr (X, Y )
(h) Are X...
The random variable X is uniformly distributed in the interval
[0, α] for some α >...
The random variable X is uniformly distributed in the interval
[0, α] for some α > 0. Parameter α is fixed but unknown. In
order to estimate α, a random sample X1, X2, . . . , Xn of
independent and identically distributed random variables with the
same distribution as X is collected, and the maximum value Y =
max{X1, X2, ..., Xn} is considered as an estimator of α.
(a) Derive the cumulative distribution function of Y .
(b)...
Suppose that X is uniformly distributed on the interval [0,10],
Y is uniformly distributed on the...
Suppose that X is uniformly distributed on the interval [0,10],
Y is uniformly distributed on the interval [0,10], and Z is
uniformly distributed on the interval [0,10] and that they are
mutually independent.
a)find the expected value of the min(X,Y,Z)
b)find the standard deviation of the min(X,Y,Z)