10) Find the constant C > 0 so that the given function is a density of some continuous random variable X.

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Please just answer the last two parts which are:

vii

ix

Thank you.

(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.
Transcribed Image Text:(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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