For the following probability density function with b > 0: 1 x +5.0sxs a fx(x) = 0, elsewhere 5) Find the value of a such that fx(x) is a valid PDF. 6) Find the CDF fx(0.5). 7) Find the expectation E[X]. 8) Find the PDF of Z (fz(z)) such that Z = X². 9) Find the variance o?. 10) If the transformation Y = X + 5. Find E[Y].

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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For the following probability density function with b > 0:
1
,0 <x< a
X +5
0, elsewhere
fx(x) =
5) Find the value of a such that fx(x) is a valid PDF.
6) Find the CDF fx(0.5).
7) Find the expectation E[X].
8) Find the PDF of Z (fz(z)) such that Z = X².
9) Find the variance o?.
10) If the transformation Y = X + 5. Find E[Y].
Transcribed Image Text:For the following probability density function with b > 0: 1 ,0 <x< a X +5 0, elsewhere fx(x) = 5) Find the value of a such that fx(x) is a valid PDF. 6) Find the CDF fx(0.5). 7) Find the expectation E[X]. 8) Find the PDF of Z (fz(z)) such that Z = X². 9) Find the variance o?. 10) If the transformation Y = X + 5. Find E[Y].
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