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Unformatted text preview: 100 be independent variables each with a uniform distribution on (-1 , 1). Suppose all the 300 X s, Y s, Z s are independent. i) Is 100 X i =1 X i exactly normal? If not, why not? ii) Is 100 X i =1 Y i exactly normal? If not, why not? iii) Is 100 X i =1 Z i exactly normal? If not, why not? iv) Estimate P ( 100 X i =1 X i Y i Z i > 10), in terms of the standard normal distribution function. v) Find P ( 100 Y i =1 X i 100 Y i =1 Y i 100 Y i =1 Z i > 0). 4. A die is rolled until two sixes in a row come up. Find the expected number of rolls and the expected total of all the numbers rolled. Also ﬁnd the distribution of the number of sixes rolled and the distribution of the number of ﬁves rolled....
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- Spring '09
- Math, Probability theory, probability density function, Let X1, yi zi, Xi Yi Zi