Question

4. Given that X has the probability distribution f(x) = (1/8) \binom{3}{x} for x = 0, 1, 2, and 3, find the (i) moment-generating function of this random variable and use it to determine. (ii)E(X), (iii) E(X²),

          4. Given that X has the probability distribution
f(x) = (1/8) \binom{3}{x} for x = 0, 1, 2, and 3,
find the
(i) moment-generating function of this random variable
and use it to determine.
(ii)E(X),
(iii) E(X²),

4. Given that X has the probability distribution
f(x) = (1/8) 3x for x = 0, 1, 2, and 3,
find the
(i) moment-generating function of this random variable
and use it to determine.
(ii)E(X),
(iii) E(X²),

Added by Leah S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Willis James

11/10/2021

Step 1

f(x) = (1/8) C(3,x) for x = 0,1,2,3. Since sum_{x=0}^3 C(3,x) = 8, this is a valid distribution and is Binomial(n=3, p=1/2) because P(X=x) = C(3,x) (1/2)^3 = C(3,x)/8. Show more…

Show all steps

Thanks for your feedback!

. 4. Given that x has the probability distribution f(x)=((1)/(8))([3],[x]) for x=0,1,2, and 3, find the (i) moment-generating function of this random variable and use it to determine. (ii) E(x), 4.Given that X has the probability distribution fx=1/83 for x =0, 1, 2, and 3. find the i) moment-generating function of this random variable and use it to determine (ii)E(X), (iii) E(X)