| Line 3: | Line 3: | ||
* Suppose f<sub>Q</sub>(q)= 2q for 0<q<1 | * Suppose f<sub>Q</sub>(q)= 2q for 0<q<1 | ||
* If Q = q then P(H|Q=q) = q | * If Q = q then P(H|Q=q) = q | ||
| − | |||
* Below graph: | * Below graph: | ||
f<sub>Q</sub>(q) vs q | f<sub>Q</sub>(q) vs q | ||
| Line 10: | Line 9: | ||
'''Question:''' | '''Question:''' | ||
* Suppose you take a coin from the Random Coin Machine and toss is. What is the probability of flipping a heads? | * Suppose you take a coin from the Random Coin Machine and toss is. What is the probability of flipping a heads? | ||
| − | |||
'''Answer:''' | '''Answer:''' | ||
Revision as of 04:42, 11 October 2008
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 fQ(q)= 2q for 0<q<1
- If Q = q then P(H|Q=q) = q
- Below graph:
fQ(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
