(20) Graduate student only. Let V and W be discrete random variables defined on some probability...

 

Transcribed Image Text:

(20) Graduate student only. Let V and W be discrete random variables defined on some probability space with a joint pmf Pvw(vw) a. Prove that E[v+w] =E[v]+E[w]. Do not assume independence. b. Prove that if V and W are independence, then E[V*W] =E[v]*E[w] c. Assume that V and W are independence and variance of and o. Show that the variance of V+W is o+w = 0 + 0 | (20) Graduate student only. Let V and W be discrete random variables defined on some probability space with a joint pmf Pvw(vw) a. Prove that E[v+w] =E[v]+E[w]. Do not assume independence. b. Prove that if V and W are independence, then E[V*W] =E[v]*E[w] c. Assume that V and W are independence and variance of and o. Show that the variance of V+W is o+w = 0 + 0 |

Answer rating: 100% (QA)

a To prove that EVW EV EW without assuming independence we use the definition of expected value for ... View the full answer