# 100AHW5 - X 520? (2) What is the probability that X...

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STAT 100A HWV Due next Wed Problem 1: For both discrete and continuous cases, prove (1) E[ a + bX ] = a + b E[ X ]. (2) Var[ a + bX ] = b 2 Var[ X ]. Problem 2: For both discrete and continuous cases, prove Var[ X ] = E[ X 2 ] - E[ X ] 2 . Problem 3: For U Uniform[0 , 1], calculate E[ U ], E[ U 2 ], and Var[ U ]. Problem 4: For T Exponential( λ ), (1) Calculate F ( t ) = P ( T t ). (2) Calculate E[ T ]. Problem 5: Suppose Z N(0 , 1). Calculate E[ Z ] and Var[ Z ]. Problem 6: Suppose we ﬂip a fair coin 1000 times independently. Let X be the number of heads. (1) What is the probability that 480
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Unformatted text preview: X 520? (2) What is the probability that X &amp;gt; 530? Problem 7: Suppose among the population of voters, 1/3 of the people support a candidate. If we sample 1000 people from the population, and let X be the number of supporters of this candidate among these 1000 people. Let p = X/n be the sample proportion. (1) What is the probability that p &amp;gt; . 35? (2) What is the probability that p &amp;lt; . 3? 1...
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## This note was uploaded on 01/27/2011 for the course STATISTICS 100a taught by Professor Cristou during the Winter '10 term at UCLA.

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