| Line 1: | Line 1: | ||
| − | + | [[Category:ECE302Fall2008_ProfSanghavi]] | |
| + | [[Category:probabilities]] | ||
| + | [[Category:ECE302]] | ||
| + | [[Category:problem solving]] | ||
| + | |||
| + | =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 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<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: f<sub>Q</sub>(q) vs q | * Below graph: f<sub>Q</sub>(q) vs q | ||
| − | * [[Image: | + | * [[Image:RVCoinMach_ECE302Fall2008sanghavi.JPG]] |
| − | + | =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= | |
* P(H) <math>= \int_{0}^{1}P(H|Q=q) * fQ(q) dq</math><br> <math>= \int_{0}^{1}q^2*q dq</math><br> = <math>= 2/3 | * P(H) <math>= \int_{0}^{1}P(H|Q=q) * fQ(q) dq</math><br> <math>= \int_{0}^{1}q^2*q dq</math><br> = <math>= 2/3 | ||
| + | ---- | ||
| + | [[Main_Page_ECE302Fall2008sanghavi|Back to ECE302 Fall 2008 Prof. Sanghavi]] | ||
Revision as of 13:24, 22 November 2011
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 ---- [[Main_Page_ECE302Fall2008sanghavi|Back to ECE302 Fall 2008 Prof. Sanghavi]] $
