Solution Found!
Determine the value of c such that the function satisfies
Chapter 5, Problem 13E(choose chapter or problem)
Determine the value of c such that the function f(x,y) = cxy for 0 < x < 3 and 0 < y < 3 satisfies the properties of a joint probability density function.
Determine the following:
(a) P(X < 2, Y < 3)
(b) P(X < 2.5)
(c) P(1 < Y < 2.5)
(d) P(X > 1.8, 1 < Y < 2.5)
(e) E(X)
(f) P(X < 0, Y < 4)
(g) Marginal probability distribution of X
(h) Conditional probability distribution of Y given that X = 1 5.
(i) E(Y | X) =1.5)
(j) P(Y < 2 | X =1.5)
(k) Conditional probability distribution of X given that Y = 2
Questions & Answers
QUESTION:
Determine the value of c such that the function f(x,y) = cxy for 0 < x < 3 and 0 < y < 3 satisfies the properties of a joint probability density function.
Determine the following:
(a) P(X < 2, Y < 3)
(b) P(X < 2.5)
(c) P(1 < Y < 2.5)
(d) P(X > 1.8, 1 < Y < 2.5)
(e) E(X)
(f) P(X < 0, Y < 4)
(g) Marginal probability distribution of X
(h) Conditional probability distribution of Y given that X = 1 5.
(i) E(Y | X) =1.5)
(j) P(Y < 2 | X =1.5)
(k) Conditional probability distribution of X given that Y = 2
ANSWER:Step 1 of 12
Given that,
The probability density function is given by,
Now,
The value c is to be determined such that the probability density function follows the following property:
Then,
The required value of c is 
Therefore, the probability density function is:
