Week_3_Practice_Problems

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 fy y y = −> . Find a) (0 1) PY << b) for any () ( ) Sy PY y => 0 y > c) Suppose are 5 independent copies of Y and let 1 ,..., YY 5 Y 15 min{ ,. .., } VY = . Find the pdf of V by first finding ( ) PV v > 2. Suppose . ~ (0,1) ZG a) Find and ( 1.87) PZ > (| | 2) > b) If , find 32 YZ =+ (2 4) < < and (| 2 | 1) > c) What is the distribution of 24 * WY = ? 3. A model to describe the repeated measurement of a variate on a unit is 1 , ~ (0,0.02), ,..., independent ii i n YR R G R R θ where 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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Week_3_Practice_Problems - Week 3 Practice Problems (Review...

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