Question

Find the characteristic function of the random variable, (jv) e[exp(jvx)]

a) 1 - jv
b) e^(jv)
c) 1 + jv
d) e^(-jv)

Answer 1

The characteristic function of the random variable (jv) e^(jvx) is e^(-vx).

Step-by-step explanation:

The characteristic function of a random variable X is defined as the expected value of the complex exponential function with the variable multiplied by the random variable, i.e., E(exp(jvX)). In this case, the random variable is (jv) multiplied by e^(jvx).

To find the characteristic function, we substitute the random variable into the expected value formula and simplify: E(exp(jv(jv)e^(jvx))) = E(e^(-vx)).

The characteristic function of the random variable (jv) e^(jvx) is e^(-vx). Hence, the correct answer is d) e^(-jv).