hw08 - x . Sketch F X ( x ). (vi) (2 pts.) Find the value b...

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ENEE 324 ASSIGNMENT 8 Due Tue 10/06 The probability density function (pdf) of a continuous random variable X is given by f X ( x ) = cx , 0 x 1 cx - 2 , x > 1 0 , x < 0 (i) (2 pts.) Sketch f X ( x ). What is the range of values of X ? (ii) (2 pts.) What is the value of c ? (iii) (3 pts.) For a [0 , 1], determine the probability that X a . (iv) (3 pts.) For a > 1, determine the probability that X > a . (v) (4 pts.) Using your answers to (i)–(iv) above, determine the cdf F X ( x ) for every
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Unformatted text preview: x . Sketch F X ( x ). (vi) (2 pts.) Find the value b such that 4 P [ X b ] = P [ X &gt; b ]. (vii) (4 pts.) Explain how, with the help of a fair coin, you can use the random variable X to generate random variable Y with pdf proportional to the function f ( x ) = ( | x | , | x | 1 | x |-2 , | x | &gt; 1 What is the constant of proportionality, i.e., the ratio f Y ( ) /f ( )?...
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