Unformatted text preview: Assume that the appropriate probability densities for Y 1 and Y 2 are f 1 ( y 1 ) = 6 y 1 (1 − y 1 ), ≤ y 1 ≤ 1, 0, elsewhere f 2 ( y 2 ) = 3 y 2 2 , ≤ y 2 ≤ 1, 0, elsewhere The proportion of the sample volume due to type A crystals is then Y 1 Y 2 . Assume that Y 1 and Y 2 are independent. Find the probability density of U = Y 1 Y 2 . 2. Suppose Y 1 is normally distributed with mean 5 and variance 1 and Y 2 is normally distributed with mean 4 and variance 3. If Y 1 and Y 2 are independent, find P(Y 1 > Y 2 ). 3. If Y is a continuous random variable and m is the median of the distribution, then m is such that P(Y ≤ m ) = P(Y ≥ m ) = 1/2. Let Y 1 , Y 2 , . .., Y n be independent, exponentially distributed random variables with mean β and median m . Find P(Y ( n ) > m ). 1...
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 Fall '09
 Snyder
 Math, Statistics, Normal Distribution, Probability theory, probability density function, y1

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