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 the discrete random variable, x, have the following
probability mass function
f(x)= c|x-2|, x=-2,-1,0,1,2,3
a....
let the discrete random variable, x, have the following
probability mass function
f(x)= c|x-2|, x=-2,-1,0,1,2,3
a. find the constant such that fx is a valid pmf
b. find P(|X-1|>1)
c. find the expected value of X
d. find the expected value of X^2
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)