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 jinydu 2003-12-13 02:04

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.

 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 [B]one[/B] 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.

[url]http://psych.rice.edu/online_stat/chapter5/binomial.html[/url]

[url]http://cnx.rice.edu/content/m11024/latest/[/url]

 Orgasmic Troll 2003-12-13 02:58

X is a random variable with binomial distribution

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

(N,n)*p[sup]n[/sup]q[sup]N-n[/sup] = N!/n!(N-n)! * p[sup]n[/sup](1-p)[sup]N-n[/sup]

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

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