Week_3_Practice_Problems - Week 3 Practice Problems(Review...

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Week 3 Practice Problems (Review continuous random variables and their properties + likelihoods for discrete variates) 1. Suppose Y is an exponential random variable with pdf ( ) exp{ / 2}/ 2, 0 f y y y = > . Find a) (0 1) P Y < < b) for any ( ) ( ) S y P Y y = > 0 y > c) Suppose are 5 independent copies of Y and let 1 ,..., Y Y 5 Y 1 5 min{ ,..., } V Y = . Find the pdf of V by first finding ( ) P V v > 2. Suppose . ~ (0,1) Z G a) Find and ( 1.87) P Z > (| | 2) P Z > b) If , find 3 2 Y Z = + (2 4) P Y < < and (| 2 | 1) P Y > c) What is the distribution of 2 4* W Y = ? 3. A model to describe the repeated measurement of a variate on a unit is 1 , ~ (0,0.02), ,..., independent i i i n Y R R G R R θ = + where θ represents the true value of what is being measured and i R the “measurement error” on the i th measurement. a) For any single measurement, what is the chance that the measured value differs from the true value by more than one standard deviation? b) Suppose . What is the chance that both measured values differ from the true value by more than one standard deviation?
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