# Distributions question

Please try and explain the approach as well. Will post the answer soon. Thanks in advance to all of you. Let X be a uniformly distributed random variable between minus one and one so that the standard deviation of X is 0.577. What percentage of the distributions will be less than 1.96 standard deviations above the mean: a. 100% b. 97.5% c. 95% d. Insufficient information provided.

I think the answer is a though I am not sure. My approach is that 1.96*sigma = 1.96*0.577=1.13. Since X lies between 1 and -1, 100% of the distribution is less than 1.96 standard deviations above the mean

Yes answer is A. Great explanation. So let us assume that the volatility was given as 0.4, then 1.96*sigma would have been 0.4*1.96 = 0.784. Now would the answer have been 1.784/2*100 = 89.2% ?? Is my understanding correct?

No. If that was the case the answer would be .784.

Wyantjs, remember that X is a uniformly distributed random variable *between minus one and one*. So how I approached was: (0.784-(-1))/(1-(-1)) = 89.2% I guess you did not take into account the portion -1

anupamjain008 Wrote: ------------------------------------------------------- > Yes answer is A. Great explanation. > > So let us assume that the volatility was given as > 0.4, then 1.96*sigma would have been 0.4*1.96 = > 0.784. Now would the answer have been 1.784/2*100 > = 89.2% ?? > > Is my understanding correct? You can’t arbitrary change standard deviation. It would make more sense to ask the same question using 1.36 standard deviations while keeping the same standard deviation. (1.36*0.577 = 1.96*0.4=0.784). Now if you ask the question, what percentage of the distribution would be less than 1.36 standard deviations above the mean, the answer would be (1+0.784)/(1-(-1))=1.784/2=0.108 = 89.2%

No, I was not incorrect. Maratikus is also correct. If X is uniform on [-1,1], it has a variance of .33, and std. dev. of .57. This is a fact, and we cannot just change this or assume it is otherwise.

Cool… thanks a lot guys.

Anupam, in the first place if -1

To add, what Maratikus said is right. 