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You have 2 coins and a spinning pointer U. The coins are fair and unbiased, and the pointer U has a uniform distribution over [0, 1). You flip the both coins and spin the pointer. A random variable X is defined as follows: If the first coin is "heads", then:

423_e5564d81-bb3f-4eb7-a15c-b777545fe5b8.png

If the first coin is "tails", then X = U + 2. Define another random variable:

760_fb749c83-57a1-439f-857f-e5e7484e19ab.png

(a) Find FX(x).

(b) Find P r( ½ ≤ X ≤ 2½ ).

(c) Sketch the pdf of Y and label important values.

(d) Design an optimal detection rule to estimate U if you are given only Y. What is the probability of error?

(e) State how to, or explain why it is not possible to:

i. Generate a binary random variable Z, pZ(1) = p, given U?

ii. Generate a continuous, uniformly distributed random variable given Z?

Electrical & Electronics, Engineering

  • Category:- Electrical & Electronics
  • Reference No.:- M91972994

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