Help with Math Problem

jinydu · 2003-12-13, 02:04

I'm preparing for a Math Exam next Monday and this is a problem on a Past Paper. Could someone help me out (but don't provide the answer, just a hint please)?

A coin is biased so that when it is tossed the probability of obtaining heads is 2/3. The coin is tossed 1800 times. Let X be the number of heads obtained. Find:

a) The mean value of X

b) The standard deviation of X

Of course, a) is easy to find. The mean of X = (2/3)*1800 = 1200.

wblipp · 2003-12-13, 02:41

There is a simple and well known formula for the variance of binomial distribution - you should probably look it up and memorize it for the exam. If you must derive it, then find the variance of the outcome for flipping the coin one time, then note that 1800 flips is the sum of 1800 iid random variable, so their variances add.

dsouza123 · 2003-12-13, 02:42

Hope this helps.

http://psych.rice.edu/online_stat/ch.../binomial.html

http://cnx.rice.edu/content/m11024/latest/

Orgasmic Troll · 2003-12-13, 02:58

X is a random variable with binomial distribution

The probabilty of getting n heads out of N trials with a coin that has probabilty p of coming up heads (and probabilty q=1-p of getting tails) is

(N,n)*pⁿq^N-n = N!/n!(N-n)! * pⁿ(1-p)^N-n

where (N,n) is a binomial coefficient

the standard deviation is Sqrt[N*p*(1-p)]

Sorry if I gave too much away

jinydu · 2003-12-13, 06:00

A little too much. Oh well, I have the answer now. The standard deviation is 20. Thanks

2003-12-13, 02:04	#1
jinydu Dec 2003 Hopefully Near M48 6DE₁₆ Posts	Help with Math Problem I'm preparing for a Math Exam next Monday and this is a problem on a Past Paper. Could someone help me out (but don't provide the answer, just a hint please)? A coin is biased so that when it is tossed the probability of obtaining heads is 2/3. The coin is tossed 1800 times. Let X be the number of heads obtained. Find: a) The mean value of X b) The standard deviation of X Of course, a) is easy to find. The mean of X = (2/3)*1800 = 1200.

2003-12-13, 02:42	#3
dsouza123 Sep 2002 2·331 Posts	Hope this helps. http://psych.rice.edu/online_stat/ch.../binomial.html http://cnx.rice.edu/content/m11024/latest/ Last fiddled with by dsouza123 on 2003-12-13 at 02:47

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2003-12-13, 02:41	#2
wblipp "William" May 2003 New Haven 2³·5·59 Posts	There is a simple and well known formula for the variance of binomial distribution - you should probably look it up and memorize it for the exam. If you must derive it, then find the variance of the outcome for flipping the coin one time, then note that 1800 flips is the sum of 1800 iid random variable, so their variances add.

2003-12-13, 02:58	#4
Orgasmic Troll Cranksta Rap Ayatollah Jul 2003 1010000001₂ Posts	X is a random variable with binomial distribution The probabilty of getting n heads out of N trials with a coin that has probabilty p of coming up heads (and probabilty q=1-p of getting tails) is (N,n)pⁿq^N-n = N!/n!(N-n)! pⁿ(1-p)^N-n where (N,n) is a binomial coefficient the standard deviation is Sqrt[Np(1-p)] Sorry if I gave too much away

2003-12-13, 06:00	#5
jinydu Dec 2003 Hopefully Near M48 2×3×293 Posts	A little too much. Oh well, I have the answer now. The standard deviation is 20. Thanks