Question

Consider the density function given in the table. Calculate the moment generating function of X. X 1 2 3 P(x) .2 .3 .5 .2e^{.2t}+.3e^{(.3t)}+.5e^{(.5t)} .2e^t + .3e^{2t} + .5 e^{3t} .2e^t + .3e^{-2t} + .5 * e^{-3t} e^t + e^{2t} + e^{3t}

          Consider the density function given in the table.
Calculate the moment generating function of X.
X
1
2
3
P(x)
.2
.3
.5
.2e^{.2t}+.3e^{(.3t)}+.5*e^{(.5t)}
.2e^t + .3e^{2t} + .5 * e^{3t}
.2e^t + .3e^{-2t} + .5 * e^{-3t}
e^t + e^{2t} + e^{3t}

Consider the density function given in the table.
Calculate the moment generating function of X.
X
1
2
3
P(x)
.2
.3
.5
.2e^.2t+.3e^(.3t)+.5*e^(.5t)
.2e^t + .3e^2t + .5 * e^3t
.2e^t + .3e^-2t + .5 * e^-3t
e^t + e^2t + e^3t

Added by Jaime G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Victor Salazar

04/12/2022

Step 1

Step 1: The moment generating function of a discrete random variable X is given by: $$M_X(t) = E[e^{tX}] = \sum_{x} e^{tx}P(X=x)$$ Show more…

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Consider the density function given in the table. Calculate the moment generating function of X. X 1 2 3 P(x) .2 .3 .5 .2e^{.2t}+.3e^{(.3t)}+.5*e^{(.5t)} .2e^t + .3e^{2t} + .5 * e^{3t} .2e^t + .3e^{-2t} + .5 * e^{-3t} e^t + e^{2t} + e^{3t}