QUESTION :
Given: fx,y(x,y)=be^-(x+y) for 0<x<a and
0<y<Infinity and =0 elsewhere
a) Use Property 2 to...
QUESTION :
Given: fx,y(x,y)=be^-(x+y) for 0<x<a and
0<y<Infinity and =0 elsewhere
a) Use Property 2 to determine the value of b that will make this a
valid density function. Ans: b=1/(1-e^-a)
b) Use Property 3 to determine Fx,y(x,y) Ans:
Fxy=(1-e^-x)(1-e^-y)/(1-e^-a)
c) Take the derivative of Fx,y(x,y) to show that it equals
fx,y(x,y).
ANSWERS ARE GIVEN FOR A,B JUST PROVIDE THE STEPS
Properties of Joint Distribution Functions:
2) ??,?(∞, ∞) = ?
Example Given: ??,?(?, ?) = 0.2?(? − 1)?(? −...
Using R and install.packages("MASS"), library(MASS)
1. Generate the following vector using at least two methods.
0,...
Using R and install.packages("MASS"), library(MASS)
1. Generate the following vector using at least two methods.
0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4
2. Generate the following vector.
Apple1, Banana2, Orange3, Cranberry4,
Watermelon5
3. Generate the following vector using the “rep” function.
a, a, b, b, c, c, a, a, b, b, c, c
4. In vector y = (8, 3, 5, 7, 6, 6, 8, 9, 2, 3, 9, 4, 10, 4,
11), which elements of y contains...
1). Consider the following function and point.
f(x) = x3 + x + 3; (−2,
−7)
(a)...
1). Consider the following function and point.
f(x) = x3 + x + 3; (−2,
−7)
(a) Find an equation of the tangent line to the graph of the
function at the given point.
y =
2) Consider the following function and point. See Example
10.
f(x) = (5x + 1)2; (0, 1)
(a) Find an equation of the tangent line to the graph of the
function at the given point.
y =
Using R programming language, complete the following.
1. Generate the bivariate normal sample of size 100...
Using R programming language, complete the following.
1. Generate the bivariate normal sample of size 100 with
parameters
a. marginal mean of X equal to 1,
b. marginal mean of Y equal to 2,
c. marginal variance of X equal to 3,
d. marginal variance of Y equal to 4,
e. correlation between X and Y equal to -1/2.
You can use the function mvrnorm(), first installing its package by
the code
if (! require ("MASS")) install.packages("MASS"); library
("MASS")
2....
A continuous random variable X has the following
probability density function F(x) = cx^3, 0<x<2 and...
A continuous random variable X has the following
probability density function F(x) = cx^3, 0<x<2 and 0
otherwise
(a) Find the value c such that f(x) is indeed
a density function.
(b) Write out the cumulative distribution function of
X.
(c) P(1 < X < 3) =?
(d) Write out the mean and variance of X.
(e) Let Y be another continuous random variable such
that when 0 < X < 2, and 0 otherwise. Calculate
the mean of Y.