Question

Let X have the moment generating function of Example 3.29 and let Y = X "-1. Recall that X is the number of people who need to be checked to get someone who is Rh+, so Y is the number of people checked before the first Rh+ person is found. Find MY(t) using the second proposition.

Answer #1

(i) If a discrete random variable X has a moment generating
function
MX(t) = (1/2+(e^-t+e^t)/4)^2, all t
Find the probability mass function of X. (ii) Let X and Y be two
independent continuous random variables with moment generating
functions
MX(t)=1/sqrt(1-t) and MY(t)=1/(1-t)^3/2, t<1
Calculate E(X+Y)^2

Let ? and ? be two independent random variables with moment
generating functions ?x(?) = ?t^2+2t and
?Y(?)=?3t^2+t . Determine the
moment generating function of ? = ? + 2?. If possible, state the
distribution name (and include parameter values) of the
distribution of ?.

Let X denote a random variable with probability density
function
a. FInd the moment generating function of X
b If Y = 2^x, find the mean E(Y)
c Show that moments E(X ^n) where n=1,4 is given by:

Let Mx(t) be a moment generating function. Let
Sx (t) = [Mx (t)]2− Mx
(t). Prove that S ′x(0) = µX.

Let X ∼ N(μ,σ2). Let Y = aX for some constant a. Find the joint
moment generating function of (X, Y ).

The moment generating function for the random variable X is
MX(t) = (e^t/ (1−t )) if |t| < 1. Find the variance of X.

The random variable X has moment generating function
ϕX(t)=(0.44e^t+1−0.44)^8
Provide answers to the following to two decimal places
(a) Evaluate the natural logarithm of the moment generating
function of 3X at the point t=0.4.
(b) Hence (or otherwise) find the expectation of 3X.
(c) Evaluate the natural logarithm of the moment generating
function of 3X+6 at the point t=0.4.

Let X and Y have the joint probability density function f(x, y)
= ⎧⎪⎪ ⎨ ⎪⎪⎩ ke−y , if 0 ≤ x ≤ y < ∞, 0, otherwise. (a) (6pts)
Find k so that f(x, y) is a valid joint p.d.f. (b) (6pts) Find the
marginal p.d.f. fX(x) and fY (y). Are X and Y independent?

1
Let X be an accident count that follows the Poisson distribution
with parameter of 3.
Determine:
a
E(X)
b
Var(X)
c
the probability of zero accidents in the next 5 time periods
d
the probability that the time until the next accident exceeds n
e
the density function for T, where T is the time until the next
accident
2
You draw 5 times from U(0,1). Determine the density function for...

1. Let f be the function defined by f(x) = x
2 on the positive real numbers. Find the
equation of the line tangent to the graph of f at the point (3,
9).
2. Graph the reflection of the graph of f and the line tangent to
the graph of f at the point
(3, 9) about the line y = x.
I really need help on number 2!!!! It's urgent!

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