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Probablity Question

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Probablity Question

by Utkarsh86 » Sun Mar 13, 2011 3:09 pm
5. The weekly NASDAQ return was positive 56% of the time through January 2011. Assuming a random process with this probability, with returns independent from week to week,

a. What is the probability that returns will be positive in exactly 4 out of the next 10 weeks?
b. How likely is it that there will be positive returns in more than 30 of the next 50 weeks?

All help is appreciated
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by Night reader » Sun Mar 13, 2011 4:16 pm
Although weekly events of NASDAQ returns are independent on each other, there's strong dependence on time. From my stats class I figured there many answers to your question depending which time series analysis we would perform... where did you get this question - the one is guaranteed to be out of my study scope for GMAT.

One way, though very primitive, I would approach this question by having 56 positive returns within 100 replication series. Out of 10 replications then I have 5.6 success rate, which means that the probability I have 4 positive within the next 10 weeks is very high -a)
b) could be resolved the same way, actually the one is just E (expected-average) for all data

further, various ways could be applied here, but we are missing data for some methods-exponential average :(
Utkarsh86 wrote:5. The weekly NASDAQ return was positive 56% of the time through January 2011. Assuming a random process with this probability, with returns independent from week to week,

a. What is the probability that returns will be positive in exactly 4 out of the next 10 weeks?
b. How likely is it that there will be positive returns in more than 30 of the next 50 weeks?

All help is appreciated
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by srcc25anu » Mon Mar 14, 2011 5:06 am
for part (i) is it 10c4 / 2^10 ??? (assuming nasdaq either increases or decreases in a given week - ignoring the remains constant from one week to another scenaro)
taking the third scenario into consideration i.e. it remains constant from one week to another, i think it should be 10C4 / 3^10

what's th OA?
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by HSPA » Mon Mar 14, 2011 8:53 am
a) success rate = 56/100

How to get exactly 4 out of 10 sucess rate = (4/10)(56/100) = 28/125
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