(10) Find the constant C > 0 so that the given function is a density of some continuous random variable X.(i) f (x) = cx, on [0, 1],(ii) f(x) = ce-3x, on [0, ∞),(v) f(x) = c/x³, on [1, 0),(vii) f(x) = cxe¬x² , on [0, c∞),(ix) f(x) = c sin x, on (0, t),123N/A(Select One for (i))-12N/A(Select One for (iii)1245N/A(Select One for (v)-11-22N/A(Select One for (vii))21/2T/2N/A(Select One for (ix))-/3 O3.-IN O3.

Since the questions contains many subparts as per the guidelines I am answering the first three…

Answered: (10) Find the constant c > 0 so that…

(10) Find the constant c > 0 so that the given function is a density of some continuous random variable X. ki) f(x) = cx, on [0, 1], kiii f(x) = ce-3x, on [0, ∞), v f(x) = clx,c on [1, 00), %3D

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

100%

(10) Find the constant C > 0 so that the given function is a density of some continuous random variable X.
(i) f (x) = cx, on [0, 1],
(ii) f(x) = ce-3x, on [0, ∞),
(v) f(x) = c/x³, on [1, 0),
(vii) f(x) = cxe¬x² , on [0, c∞),
(ix) f(x) = c sin x, on (0, t),
1
2
3
N/A
(Select One for (i))
-1
2
N/A
(Select One for (iii)
1
2
4
5
N/A
(Select One for (v)
-1
1
-2
2
N/A
(Select One for (vii))
2
1/2
T/2
N/A
(Select One for (ix))
-/3 O
3.
-IN O
3.

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