The random variable X~uniform(0,1) and Y~Exp(1), and they are
independent, find the distibution of Z=2X+Y. Step...
The random variable X~uniform(0,1) and Y~Exp(1), and they are
independent, find the distibution of Z=2X+Y. Step by Step please
better to have a graph and be organized before you answer
X is an independent standard uniform random variable X ∼
Uniform(0, 1)
Y is an independent standard uniform random variable Y ∼
Uniform(0, 1)
U = min(X, Y )
V = max(X, Y )
Find the correlation coefficient of V and U , ρ(U, V) =
Correlation(U, V).
Let X ∼Exp(1), Y ∼Exp(2) be independent random variables.
(a) What is the range of Z := X + Y ?
(b) Find the pdf of Z.
(c) Find MZ(t).
(d) Let U = e Y . What is the range of U?
(e) Find the pdf of U|X.
Let X,,X, and X, be independent uniform random
variables on [0,1] Write Y = X, +X, and Z = X+ X. a.) Compute
E[X,X,X,. (5 points) b.) Compute Var(X). (5 points) c.) Compute and
draw a graph of the density function fr. (15 points)
Let X, Y and Z be independent random variables, each uniformly
distributed on the interval (0,1).
(a) Find the cumulative distribution function of X/Y.
(b) Find the cumulative distribution function of XY.
(c) Find the mean and variance of XY/Z.
Let ? and ? be two independent uniform random
variables such that
?∼????(0,1) and
?∼????(0,1).
A) Using the convolution formula, find the pdf
??(?) of the random variable
?=?+?, and graph it.
B) What is the moment generating function of ??
Random variable X is a continuous uniform (0,4) random variable
and Y=X^(1/2). (Note: Y is always the positive root.)
What is the P[X>=E[X]] ?
What is the E[Y] ?
what is the P[Y>=E[Y]]?
what is the PFD of fY(y)?
1. Assume that X and Y are two independent discrete random
variables and that X~N(0,1) and Y~N(µ,σ2).
a. Derive E(X3) and deduce that E[((Y-µ)/σ)3]
= 0
b. Derive P(X > 1.65). With µ = 0.5 and σ2 = 4.0,
find z such that P(((Y-µ)/σ) ≤ z) = 0.95. Does z depend on µ and/or
σ? Why