Question: Conditional Expectation given a indicator random variable Let Y be a discrete random variable, A be an event with 0 < P(A) < 1, and

Conditional Expectation given a indicator random variable

Let Y be a discrete random variable, A be an event with 0 < P(A) < 1, and IA be the indicator random variable for A.

(a) Explain precisely how the random variable E(Y |IA) relates to the numbers E(Y |A) and E(Y |Ac ).

(b) Show that E(Y |A) = E(Y IA)/P(A), directly from the definitions of expectation and conditional expectation.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Conditional Expectation given a indicator random variable Let Y be a discrete random variable, A be an event with 0

Q:

Let X be an event and IX an associated indicator random variable. IX is 1 if a value is in event X, 0 otherwise. Let Y be an event and IY the associated indicator random variable in the same way that...

Q:

Let A be an event, and let IA be the associated indicator random variable: IA (w) = 1 if we A, and IA (w) = 0 if w & A. Similarly, let I be the indicator of another event, B. Suppose that, P (A) = p,...

Q:

Indicators: Let A be an event, and let IA be the associated indicator random variable: IA (w) = 1 if w belongs A , and IA (w) = 0 if w doesn't belong to A . Similarly, let IB be the indicator of...

Q:

Similar to the definition of the probability mass function, we can define the conditional probability mass function. The conditional probability mass function of random variable X conditioned on an...

Q:

Name:_________________________________1(point) True/False: (Each question is worth 2 points) Indicate whether the statement is true or false. ____ 1. The length of time for which an apartment in a...

Q:

subject-statistics can you please answer this all questions Question 17(1 point) The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a...

Q:

( d ) In an election, a proportion p will vote for candidate G and a proportion 1 - p will vote for candidate B . In an election poll, a number of voters are asked for whom they will vote. Let x i be...

Q:

The skewed normal distribution defines a skewed continuous random variable. Let m,s denote a normal p.d.f. with moments (m, s) and let (z) denote a standard normal c.d.f. The skewed normal can be...

Q:

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal...

Q:

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of students in a randomly selected elementary school...

Q:

Fill on the blanks Crossword 11 urine Occult 26 33 30 25 14 ACROSS 1. Urine sample collection method (two words) 6. chloride test 7. Grow microbes on nutrient media 23. 26. Related to the lung 27....

Q:

Question 8 Given the following economic information about France, Malaysia, Australia, and Switzerland, use the Absolute Version to determine the change in exchange rate between the MYR and EUR [ set...

Q:

A company is preparing completing their Cash Budget. The following data has been prepared for cash receipts and payments. January February March Cash receipts $1,061,200 $1,182,400 $1,091,700 Cash...