Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Let X have the probability mass function P(X = −1) = 1 2 , P(X = 0) = 1 3 , P(X = 1) = 1 6 Calculate E(|X|) using the approaches in (a) and (b) below. (a) First find the probability mass function of the random variable Y = |X| and using that compute E(|X|). (b) Apply formula (3.24) with g(x) = |x|. For reference, formula 3.24 states

Sagot :

ajeigbeibraheem

Answer:

Step-by-step explanation:

From the given information:

Note that the possible values of Y are 0 and 1 because;

y = 0 if X = 0 and y = 1 if X = ±1

∴

[tex]P(Y =0) = P(X = 0) =\dfrac{1}{3}[/tex]

[tex]P(Y = 1) = P(X = -1 \ or \ 1) \\ \\ = P(X = -1) + P(X = 1)[/tex]

[tex]= \dfrac{1}{2}+ \dfrac{1}{6}[/tex]

[tex]=\dfrac{3+1}{6}[/tex]

[tex]= \dfrac{2}{3}[/tex]

b)

[tex]E(|X|) = \sum |x| P(X=x) = ( 1 \times \dfrac{1}{2}) + ( 0\times \dfrac{1}{3}) + ( 1 \times \dfrac{1}{6})[/tex]

[tex]= \dfrac{2}{3}[/tex]

We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.