Discussion
Let X be a degenerate random variable, at \(X = c\). Then characteristic function of X at 't' is :
Answer: C
The characteristic function is \(\exp(itc)\).
The characteristic function is \(\varphi(t) = E(e^{itX})\). A degenerate variable takes the single value \(c\) with probability 1, so
\[ \varphi(t) = e^{itc} \]
Its modulus is 1 for every \(t\), and \(\varphi(0) = 1\) as for any characteristic function, which rules out the constants \(c\) and 0. \(\exp(-itc)\) is the complex conjugate, the characteristic function of \(-X\), or of X under the opposite sign convention, which is not the standard definition.
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