Question

Let X be a random variable with p.d.f: f(x) = { 0.3 , x = -2 0.1 , x = 0 0.4 , x = 1 0.2 , x = 3 0 , o.w The moment generating function of X is m(t) = 0.1 + 0.3e^{-2t} + 0.4e^t + 0.2e^{3t} m(t) = 0.2e^{-2t} + 0.2e^t + 0.1e^{3t} m(t) = 0.4 + 0.3e^{-2t} + 0.8e^t + 1e^{3t} none of them m(t) = 0.4 + 0.3e^{-t} + 0.1e^t + 0.1e^{3t}

          Let X be a random variable with p.d.f:
f(x) = {
0.3 , x = -2
0.1 , x = 0
0.4 , x = 1
0.2 , x = 3
0 , o.w
The moment generating function of X is
m(t) = 0.1 + 0.3e^{-2t} + 0.4e^t + 0.2e^{3t}
m(t) = 0.2e^{-2t} + 0.2e^t + 0.1e^{3t}
m(t) = 0.4 + 0.3e^{-2t} + 0.8e^t + 1e^{3t}
none of them
m(t) = 0.4 + 0.3e^{-t} + 0.1e^t + 0.1e^{3t}

Let X be a random variable with p.d.f:
f(x) =
0.3 , x = -2
0.1 , x = 0
0.4 , x = 1
0.2 , x = 3
0 , o.w
The moment generating function of X is
m(t) = 0.1 + 0.3e^-2t + 0.4e^t + 0.2e^3t
m(t) = 0.2e^-2t + 0.2e^t + 0.1e^3t
m(t) = 0.4 + 0.3e^-2t + 0.8e^t + 1e^3t
none of them
m(t) = 0.4 + 0.3e^-t + 0.1e^t + 0.1e^3t

Added by الشيخ م.

Mathematical Statistics with Applications

Dennis D. Wackerly, William Mendenhall… 7th Edition

Chapter 3

Instant Answer

Solved by Expert Bradley Duda

05/21/2024

Step 1

The moment generating function \( m(t) \) of a random variable \( X \) is defined as \( m(t) = E[e^{tX}]\), where \( E \) denotes the expectation. Show more…

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