The current I through a semiconductor diode is relative to the voltage V across the diode via the following relationship: I = 1o(e – 1) where Io is the magnitude of the reverse current. Suppose that the voltage across the diode is modeled as a continuous random variable V with probability density function (PDF) given by fv(u) = 0.5e¬lu|, -∞ < u < ∞ Then the current can also be modeled as a continuous random variable, T. Note: I is the ideal current; whereas, I is the random variable modeling the current- the same goes for V (voltage) versus V random variable. (a) What values can I take on? (b) Find the CDF of T. (c) Find the PDF of I.

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D7
The current I through a semiconductor diode is relative to the voltage V across the diode
via the following relationship:
I = Io(e – 1)
where Io is the magnitude of the reverse current. Suppose that the voltage across the diode
is modeled as a continuous random variable V with probability density function (PDF) given
by
fv(u) = 0.5e¬lul,
00 >n>∞-
Then the current can also be modeled as a continuous random variable, T.
Note: I is the ideal current; whereas, I is the random variable modeling the current-
the same goes for V (voltage) versus V random variable.
(a) What values can I take on?
(b) Find the CDF of T.
(c) Find the PDF of T.
Transcribed Image Text:The current I through a semiconductor diode is relative to the voltage V across the diode via the following relationship: I = Io(e – 1) where Io is the magnitude of the reverse current. Suppose that the voltage across the diode is modeled as a continuous random variable V with probability density function (PDF) given by fv(u) = 0.5e¬lul, 00 >n>∞- Then the current can also be modeled as a continuous random variable, T. Note: I is the ideal current; whereas, I is the random variable modeling the current- the same goes for V (voltage) versus V random variable. (a) What values can I take on? (b) Find the CDF of T. (c) Find the PDF of T.
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