Determine the value of c that makes a joint probability

Chapter 5, Problem 25E

(choose chapter or problem)

Determine the value of c that makes \(f x y z(x, y, z)=c\) a joint probability density function over the region \(x>0, y>0, z>0\), and \(x+y+z<1\).

Determine the following:

(a) \(P(X<0.5, Y<0.5, Z<0.5)\)         (b) \(P(X<0.5, Y<0.5)\)

(c) \(P(X<0.5)\)                         (d) \(E(X)\)

(e) Marginal distribution of X

(f) Joint distribution of X and Y

(g) Conditional probability distribution of X given that Y = 0.5 and Z = 0.5

(h) Conditional probability distribution of X given that Y = 0.5

Equation transcription:

Text transcription:

f x y z(x, y, z)=c

x>0, y>0, z>0

x+y+z<1

P(X<0.5, Y<0.5, Z<0.5)

P(X<0.5, Y<0.5)

P(X<0.5)

E(X)

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back