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* Below graph: f<sub>Q</sub>(q) vs q | * Below graph: f<sub>Q</sub>(q) vs q | ||
* [[Image:RVCoinMach_ECE302Fall2008sanghavi.JPG]] | * [[Image:RVCoinMach_ECE302Fall2008sanghavi.JPG]] | ||
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=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= | ||
| − | * 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</math> |
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[[Main_Page_ECE302Fall2008sanghavi|Back to ECE302 Fall 2008 Prof. Sanghavi]] | [[Main_Page_ECE302Fall2008sanghavi|Back to ECE302 Fall 2008 Prof. Sanghavi]] | ||
Latest revision as of 13:25, 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 $
