4. The discrete random variable X that has the probability distribution f(x) = 2 (1/3)* for x =1, 2, 3, .. i. Find the moment generating function determine the values of u'i determine the values of u';

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Probability & Statistics 1

**4.** The discrete random variable \( X \) has the probability distribution
\[ f(x) = 2 \left( \frac{1}{3} \right)^x \quad \text{for } x = 1, 2, 3, \ldots \]

i. Find the moment generating function.

ii. Determine the values of \(\mu'_1\).

iii. Determine the values of \(\mu'_2\).
Transcribed Image Text:**4.** The discrete random variable \( X \) has the probability distribution \[ f(x) = 2 \left( \frac{1}{3} \right)^x \quad \text{for } x = 1, 2, 3, \ldots \] i. Find the moment generating function. ii. Determine the values of \(\mu'_1\). iii. Determine the values of \(\mu'_2\).
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