Question

Let X denotes the number of correct answers for part (I) and Y denotes the number of correct answers in true/false part. Find the joint probability distribution function fX,Y(x,y)

Answer #1

I) 3 questions have four multiple choices a, b, c and d
II) only one question is true and false
Let X
denotes the number of correct answers for part (I) and
Y denotes the number of correct answers in true/false
part. Find the joint probability distribution function
fX,Y(x,y)

There is a quiz which contains 4 questions as follow:
I) 3 questions have four multiple choices a, b, c and d
II) only one question is true and false
Let XX denotes the number of correct answers for part (I) and YY
denotes the number of correct answers in true/false part. Find the
joint probability distribution function fX,Y(x,y)

There is an exam which contains 4 questions as
follow:
I) 3 questions have four multiple choices a, b, c and
d
II) only one question is true and false
Let XX denotes the number of correct answers for part
(I) and YY denotes the number of correct answers in true/false
part. Find the joint probability distribution function fX,Y(x,y

There is an ex which contains 4 questions as follow:
I) 3 questions have four multiple choices a, b, c and d
II) only one question is true and false
Let \ (X \) denotes the number of correct answers for
part (I) and \ (Y \) denotes the number of correct
answers in true / false part. Find the joint probability
distribution function \ (f_X, _Y (x, y) \)

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?

Let X and Y be a random variables with the joint probability
density function fX,Y (x, y) = { e −x−y , 0 < x, y < ∞ 0,
otherwise } . a. Let W = max(X, Y ) Compute the probability density
function of W. b. Let U = min(X, Y ) Compute the probability
density function of U. c. Compute the probability density function
of X + Y .

1. Let (X; Y ) be a continuous random vector with joint
probability density function
fX;Y (x, y) =
k(x + y^2) if 0 < x < 1 and 0 < y < 1
0 otherwise.
Find the following:
I: The expectation of XY , E(XY ).
J: The covariance of X and Y , Cov(X; Y ).

Let X and Y be a random variables with the joint probability
density function fX,Y (x, y) = { cx2y, 0 < x2 < y < x for
x > 0 0, otherwise }. compute the marginal probability density
functions fX(x) and fY (y). Are the random variables X and Y
independent?.

You throw a four sided symmetric die, if X denotes the number
you get on top you receive 2X dollars. However, to play this game
you need to pay 4 dollars to begin with. Let Y denote your win in
one throw. Find E(Y) in two different ways. i.e. using the
probability distribution function of Y and using E(X)

part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the partial derivatives of the function
f(x,y)=x^6y^6/x^2+y^2
fx(x,y)=
fy(x,y)=
part 3)
Find all first- and second-order partial derivatives of the
function f(x,y)=2x^2y^2−2x^2+5y
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 4)
Find all first- and second-order partial derivatives of the
function f(x,y)=9ye^(3x)
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 5)
For the function given below, find the numbers (x,y) such that
fx(x,y)=0 and fy(x,y)=0
f(x,y)=6x^2+23y^2+23xy+4x−2
Answer: x= and...

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