Let Z be the random variable with support SZ = {1,2,3} and pmf
f(z) = z/6,...
Let Z be the random variable with support SZ = {1,2,3} and pmf
f(z) = z/6, for z ∈ SZ .
(a) Find the MGF (moment generating function) of Z,
Mz(t).
(b) Using Mz(t), calculate E[z^3].
Let f(x)=c(4/9)^x. Find c such that f represents the pmf of a
random variable whose possible...
Let f(x)=c(4/9)^x. Find c such that f represents the pmf of a
random variable whose possible values are 1, 2, 3, ... .
A.4/5
B.5/4
C.4/9
The above random variable is:
A.Geom(4/5) random variable
B.Bern(4/9) random variableC
c.Geom(5/9) random variable
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...
1. Let X be a discrete random variable with the probability mass
function P(x) = kx2...
1. Let X be a discrete random variable with the probability mass
function P(x) = kx2 for x = 2, 3, 4, 6.
(a) Find the appropriate value of k.
(b) Find P(3), F(3), P(4.2), and F(4.2).
(c) Sketch the graphs of the pmf P(x) and of the cdf F(x).
(d) Find the mean µ and the variance σ 2 of X. [Note: For a
random variable, by definition its mean is the same as its
expectation, µ = E(X).]
1. Suppose a random variable X has a pmf
p(x) = 3^(x-1)/4^x , x = 1,2,......
1. Suppose a random variable X has a pmf
p(x) = 3^(x-1)/4^x , x = 1,2,...
(a) Find the moment generating function of X.
(b) Give a realistic example of an experiment that this random
variable can be defined from its sample space.
(c) Find the mean and variance of X.
Let X be a discrete random variable with the pmf
p(x): 0.8 for x=-4,
0.1 for...
Let X be a discrete random variable with the pmf
p(x): 0.8 for x=-4,
0.1 for x=-2,
0.07 for x=0,
0.03 for x=2
a) Find E(2/X)
b) Find E(lXl)
c) Find Var(lXl)