By definition the characteristic function of a r.v. X is...Find characteristic functions of
1. The random variable X uniformly distributed on[-1..1]
2. The random variable Y distributed exponentially (with exponent λ)
3. The random variable Z=X+Y
Your solution of the point 2. is correct...Point 1.i got= sint/t
point 2. I found out = λ/(it- λ)
would please help me to do point 3.
As preliminary consideration I have to precise that if someone wants to operate in advanced probability, knowledge of advanced calculus, that includes complex variable function theory, convolution, Laplace and Fourier Transforms is essential. The 'final answer' to point 3 is the evaluation of the charactristic function of the r.v. Z, the p.d.f. of which is given by...NO, I cannot proceed alone. im confused.
how did you get point 3, 4 and 5. is point 5 the final answer?
and how did you change to to s in point 3 and 4