3. Let f: R2R be a function defined by f(x, y): = [2, if 0≤x≤ 1,0 ≤ y ≤ x; elsewhere. 0, (This function is called the joint probability density function of random variables X and Y.) (a) Evaluate the following: g(a) = f* f(x, y) dy for 0 ≤ x ≤ 1 and h(y) = [₁² 1 [ f(x, y) dx for 0 ≤ y ≤ 1. (Then the marginal probability density function of X and Y is given by [g(x), if 0≤x≤1; Sh(y), if 0 ≤ y ≤ 1; fx(x) = respectively.) 1 otherwise, otherwise. and fy (y) = = = [[_xyf(x,y) dy dx, and Cov(X, Y) := (b) Evaluate the following: E(X), E(Y), E(XY) := E(XY) E(X) E(Y).
3. Let f: R2R be a function defined by f(x, y): = [2, if 0≤x≤ 1,0 ≤ y ≤ x; elsewhere. 0, (This function is called the joint probability density function of random variables X and Y.) (a) Evaluate the following: g(a) = f* f(x, y) dy for 0 ≤ x ≤ 1 and h(y) = [₁² 1 [ f(x, y) dx for 0 ≤ y ≤ 1. (Then the marginal probability density function of X and Y is given by [g(x), if 0≤x≤1; Sh(y), if 0 ≤ y ≤ 1; fx(x) = respectively.) 1 otherwise, otherwise. and fy (y) = = = [[_xyf(x,y) dy dx, and Cov(X, Y) := (b) Evaluate the following: E(X), E(Y), E(XY) := E(XY) E(X) E(Y).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:10:25 PM Tue Apr 18
T
3. Let ƒ: R² → R be a function defined by
2,
0,
f(x, y) =
=
●●●
ƒx(x) =
=
if 0 ≤ x ≤ 1,0 ≤ y ≤ x;
elsewhere.
(This function is called the joint probability density function of random variables X and Y.)
1
(a) Evaluate the following: g(a) = ["* f(x, y) dy for 0 ≤ x ≤ 1 and h(y) = f f(x, y) dx
0
for 0 ≤ y ≤ 1. (Then the marginal probability density function of X and Y is given by
[g(x), if 0≤x≤ 1;
ſh(y), if 0≤ y ≤1;
respectively.)
0,
otherwise,
otherwise.
and fy (y) =
=
0₂
9
(b) Evaluate the following: E(X), E(Y), E(XY) := - ff =
xyf (x, y) dy dx, and Cov(X, Y)
E(XY) – E(X) E(Y).
+
11% 0
<
213
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