Set-Up

• Suppose you have a machine that produces random coins. (Thus, the probability of taking a coin from the machine, tossing it, and getting a 'heads' is a random variable.
• Suppose f_Q(q)= 2q for 0<q<1
• If Q = q then P(H|Q=q) = q
• Below graph: f_Q(q) vs q
• 

Question

• Suppose you take a coin from the Random Coin Machine and toss is. What is the probability of flipping a heads?

Answer

• P(H) $ = \int_{0}^{1}P(H|Q=q) * fQ(q) dq $
  $ = \int_{0}^{1}q^2*q dq $
  = $ = 2/3 ---- [[Main_Page_ECE302Fall2008sanghavi|Back to ECE302 Fall 2008 Prof. Sanghavi]] $