hw09 - ˜ F x = F X x 2 Is it the cdf of a random variable...

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ENEE 324 ASSIGNMENT 9 Due Thu 10/08 The probability density function (pdf) of a continuous random variable X is given by f X ( x ) = cx 2 e - x/ 2 u ( x ) where u ( x ) is the unit step at x = 0 and c > 0. (i) (3 pts.) Determine the value of x which maximizes f X ( x ). Sketch f X ( x ). (ii) (3 pts.) What is the value of c ? ( Integrate by parts or look up standard integrals, e.g., on mathworld.wolfram.com ) (iii) (3 pts.) Determine P [ X > x ] for every x 0. (iv) (2 pts.) Write an equation for the cdf F X ( x ). (v) (5 pts.) Consider the function
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Unformatted text preview: ˜ F ( x ) = ( F X ( x )) 2 Is it the cdf of a random variable? If so, what is the corresponding pdf ˜ f ( x )? (vi) (4 pts.) Explain how, with the help of a biased coin with probabilities 3/5 and 2/5 for H and T respectively, you can use X to generate a random variable Y with pdf f Y ( x ) = 3 c 5 · x 2 e-x/ 2 u ( x ) + 2 5 · δ ( x + 2) (where c is the value found in part (i))....
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