Problem 4: Suppose the random variable X in Problem 3 is sent through a quantizer g(x) to produce the random variable Y = g(X), where * < -0.5, 0, -0.5 <* < 0.5, r 2 0.5. -1, g(r) (a) Find a mathematical expression for Fy(y), the CDF of Y. (b) Find a mathematical expression for fy (y), the PDF of Y. (c) Find the value of E[Y].
Problem 4: Suppose the random variable X in Problem 3 is sent through a quantizer g(x) to produce the random variable Y = g(X), where * < -0.5, 0, -0.5 <* < 0.5, r 2 0.5. -1, g(r) (a) Find a mathematical expression for Fy(y), the CDF of Y. (b) Find a mathematical expression for fy (y), the PDF of Y. (c) Find the value of E[Y].
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Author:Robert L. Boylestad
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![Problem 4: Suppose the random variable X in Problem 3 is sent through a
quant izer g(r) to produce the random variable Y = g(X), where
x < -0.5,
0, -0.5 <* < 0.5,
x 2 0.5.
-1,
g(x)
(a) Find a mathematical expression for Fy (y), the CDF of Y.
(b) Find a mathematical expression for fy (y), the PDF of Y.
(c) Find the value of E[Y].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbddf1426-a28f-4b9c-96ed-ee115a37a4b2%2Fcd792278-3146-460d-a667-437f6227cfb4%2Fmvoji35_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 4: Suppose the random variable X in Problem 3 is sent through a
quant izer g(r) to produce the random variable Y = g(X), where
x < -0.5,
0, -0.5 <* < 0.5,
x 2 0.5.
-1,
g(x)
(a) Find a mathematical expression for Fy (y), the CDF of Y.
(b) Find a mathematical expression for fy (y), the PDF of Y.
(c) Find the value of E[Y].
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
a) For the given F(x) function, we have here:
Fx(-0.5) = 0.2*(1 - 0.5)2 = 0.05
Fx(0.5) = 0.5*(1 + 0.5) = 0.75
Therefore, the CDF for Y here is given as:
This is the required CDF here.
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