Q#1: The probability density of a discrete random variable X is f(x) = (()*)** Find E(X), E(X²), Var(X), and SD (X) x=0.1.2.3
Q#1: The probability density of a discrete random variable X is f(x) = (()*)** Find E(X), E(X²), Var(X), and SD (X) x=0.1.2.3
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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![1% 11. LT211. 44
TD
Homework 7
Expected value of random variable, moments and coefficient of correlation
Q#1: The probability density of a discrete random variable X is
Find E(X), E(X²), Var(X), and SD (X)
Q#2: Given that
T(x) =))*)**
d)
Find the first four raw moments
e) Find first four moments about mean
f(x) = kx³ (1-x). 0≤x≤1
a) Find the value of k so that the function f(x) is probability density function
b) Find mean
c) Find variance
Q#3: Let X and Y have the joint p.d.f described as follows
(x, y)
f(x,y)
#4: Given
(1.1)
2
15
a) Find marginal of X [1.e. g(x)].
b) Find marginal of Y [i.e. h(y)].
c) Find E(X)
d) Find E(Y)
|||
(1.2)
4
15
Homework_07
(1.3)
3
15
f(x,y)=2-x-y.
e) Find the first four raw moments.
f) Find first four moments about mean.
g)
Find the correlation coefficient between X and Y. Interpret the result.
x = 0,1,2,3
(2,1)
1
15
O
0≤x≤ 1. 0sys1
a) Find marginal of X [t.e. g(x)].
b) Find marginal of Y [i.e. h(y)].
c) Find E(X)
d) Find E(Y)
e) Find the first four raw moments.
f) Find first four moments about mean.
g) Find the correlation coefficient between X and Y. Interpret the result.
& Bb ١٢:٤٩
(2,2)
1
15
(2,3)
4
15
↑](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69c1c745-92e9-480d-90d2-08960c47427f%2F6bb6e102-10bd-4246-b968-52ad1f52539a%2F1bc73ug_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1% 11. LT211. 44
TD
Homework 7
Expected value of random variable, moments and coefficient of correlation
Q#1: The probability density of a discrete random variable X is
Find E(X), E(X²), Var(X), and SD (X)
Q#2: Given that
T(x) =))*)**
d)
Find the first four raw moments
e) Find first four moments about mean
f(x) = kx³ (1-x). 0≤x≤1
a) Find the value of k so that the function f(x) is probability density function
b) Find mean
c) Find variance
Q#3: Let X and Y have the joint p.d.f described as follows
(x, y)
f(x,y)
#4: Given
(1.1)
2
15
a) Find marginal of X [1.e. g(x)].
b) Find marginal of Y [i.e. h(y)].
c) Find E(X)
d) Find E(Y)
|||
(1.2)
4
15
Homework_07
(1.3)
3
15
f(x,y)=2-x-y.
e) Find the first four raw moments.
f) Find first four moments about mean.
g)
Find the correlation coefficient between X and Y. Interpret the result.
x = 0,1,2,3
(2,1)
1
15
O
0≤x≤ 1. 0sys1
a) Find marginal of X [t.e. g(x)].
b) Find marginal of Y [i.e. h(y)].
c) Find E(X)
d) Find E(Y)
e) Find the first four raw moments.
f) Find first four moments about mean.
g) Find the correlation coefficient between X and Y. Interpret the result.
& Bb ١٢:٤٩
(2,2)
1
15
(2,3)
4
15
↑
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