Let X(t, 0) = cos(2nt + 0) for t€ (-0, +0)be a continuous time random process, where 0 is a continuous and uniformly distributed in [-7, 1]. (a) Sketch the possible values of X(0,0) and X(0.25, 0). (b) Plot the region where

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Let X(t, 0) = cos(2nt + 0) for te (-0, +00)be a continuous time random process,
%3D
where 0 is a continuous and uniformly distributed in [-7, 1].
(a) Sketch the possible values of X(0,0) and X(0.25,0).
(b) Plot the region where
on the graph in (a). Find the probability
P-< x(0,0) <.
(c) Find the probability P[{-< x(0,0) <n< x(0.25,0) < 1}]. It may be useful
draw the region of {-<x(0,0) < ns x(0.25,0) <1}
on the graph in (a).
2
V2
(d) Find the conditional probability P[{- < x(0,0) < I< x(0.25,0) < 1}]. It
may be useful draw the region of {-< X(0,0) <|< x(0.25,0) < 1} on the
graph in (a).
Hint. For this question, find the equivalent events in terms of 0.
Transcribed Image Text:Let X(t, 0) = cos(2nt + 0) for te (-0, +00)be a continuous time random process, %3D where 0 is a continuous and uniformly distributed in [-7, 1]. (a) Sketch the possible values of X(0,0) and X(0.25,0). (b) Plot the region where on the graph in (a). Find the probability P-< x(0,0) <. (c) Find the probability P[{-< x(0,0) <n< x(0.25,0) < 1}]. It may be useful draw the region of {-<x(0,0) < ns x(0.25,0) <1} on the graph in (a). 2 V2 (d) Find the conditional probability P[{- < x(0,0) < I< x(0.25,0) < 1}]. It may be useful draw the region of {-< X(0,0) <|< x(0.25,0) < 1} on the graph in (a). Hint. For this question, find the equivalent events in terms of 0.
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