PLEASE TYPE THE ANSWER (14%) Y = -2X2 (10%) Compute / derive the PDF f Y(y)...
PLEASE TYPE THE ANSWER
(14%) Y = -2X2
- (10%) Compute / derive the PDF f Y(y) for Y = -2X2 when X is uniformly distributed over [-1, 3]. Show the range where f Y(y) is nonzero, i.e. [a, b], what is a and what is b?
(b) 4%) Verify the PDF f Y(y) you calculated in (a) is a PDF
Homework Answers
We have the PDF of 
is
.
a) Consider the tranformation 
.
The PDF of the tranformation 
is
The summation is over the number of inverse functions.
Here 
. The PDF of
is
Hence ![[a, b] = [-18, -2]](http://img.homeworklib.com/questions/5f585820-5394-11eb-ad2b-af678f293369.png?x-oss-process=image/resize,w_560)
b) To verify that 
is a PDF,
Hence
is a valid PDF.
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PLEASE TYPE THE ANSWER
(14%) Y = -2X2
(10%) Compute / derive the PDF f
Y(y)...
Let X1 , X, , and X3 be independent and uniformly distributed between-2 and 2. (a) Find the CDF and PDF ofYX, +2X2 (b) Find the CDF of Z-), + X, . (c) Find the joint PDF of Y and Z.(: Try the tri...
Let X1 , X, , and X3 be independent and uniformly distributed between-2 and 2. (a) Find the CDF and PDF ofYX, +2X2 (b) Find the CDF of Z-), + X, . (c) Find the joint PDF of Y and Z.(: Try the trick in Problem 2(b)
Let X1 , X, , and X3 be independent and uniformly distributed between-2 and 2. (a) Find the CDF and PDF ofYX, +2X2 (b) Find the CDF of Z-), + X, . (c)...
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3. X is a continuous RV with pdf f(x) and CDF F(x). a) Derive the dist of Y=F(X) b) Show that Z=-21n(Y) has a Gamma dist. & derive it. 4. X-i ~ cont with pdf fi(x) and CDF Fi(x), i=1, 2, , k. all independent. Define YjaFi(Xi), i=1, , k. Derive the distribution of
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Problem 3:
Problem 3: (20 points) Suppose X is a uniformly distributed continuous random variable over [1,3]. a. (10 points) If Y - 4X2, find f (y), the PDF of Y. Indicate the range for which it applies. b. (10 points) What is the expected value of Y 0 し( 4 4
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3. [10 pts.] Suppose r.v. y is uniformly distributed over (0,27) i.e. f*() = 1/2, for 0 <o<27 and 0 elsewhere. Consider the following r.v.'s: X = cos y and Y = siny. a. Prove that X and Y are orthogonal. b. Prove that X and Y are uncorrelated.
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Problem 3:
Problem 3: (20 points) Suppose X is a uniformly distributed continuous random variable over [1,3]. a. (10 points) If Y - 4X2, find f (y), the PDF of Y. Indicate the range for which it applies. b. (10 points) What is the expected value of Y 0 し( 4 4
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