Let E and F be two events with probabilities P(E) = 1/2, P(F) = 2/3 and P(E ∩F) = 1/3. Define random variables X and Y to be the indicator functions over E and F, respectively. Therefore, X will assign 1 for outcomes in E and 0 for outcomes in Ec while Y will assign 1 for outcomes in F and 0 for outcomes in Fc . (a) Find the joint distribution of X and Y . (b) Obtain the conditional distribution of X given Y .

Name: let e and f be two events with probabilities pe 12 pf 23 and pe f 13 define random variables x and y to be the indicator functions over e and f respectively therefore x will assign 1 for out 75287
Uploaded: 2022-09-30T01:32:24-08:00
Duration: 4 min 48 s
Channel: Madhur L
Description: let e and f be two events with probabilities pe 12 pf 23 and pe f 13 define random variables x and y to be the indicator functions over e and f respectively therefore x will assign 1 for out 75287

          Let E and F be two events with probabilities P(E) = 1/2, P(F) =
2/3 and P(E ∩F) = 1/3. Define random variables X and Y to be the
indicator functions over E and F, respectively. Therefore, X will
assign 1 for outcomes in E and 0 for outcomes in Ec
while Y will assign 1 for outcomes in F and 0 for outcomes in
Fc .
(a) Find the joint distribution of X and Y .
(b) Obtain the conditional distribution of X given Y .

Added by John T.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

09/30/2022

Step 1

Given: - P(E) = 1/2 - P(F) = 2/3 - P(E ∩ F) = 1/3 We need to find: - P(X=1, Y=1) - P(X=1, Y=0) - P(X=0, Y=1) - P(X=0, Y=0) From the explanation: - P(X=1, Y=1) = P(E ∩ F) = 1/3 - P(X=1, Y=0) = P(E ∩ Fc) = P(E) * P(Fc) = (1/2) * (1/3) = 1/6 - P(X=0, Y=1) = P(Ec ∩ Show more…

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Let E and F be two events with probabilities P(E) = 1/2, P(F) = 2/3 and P(E ∩F) = 1/3. Define random variables X and Y to be the indicator functions over E and F, respectively. Therefore, X will assign 1 for outcomes in E and 0 for outcomes in Ec while Y will assign 1 for outcomes in F and 0 for outcomes in Fc . (a) Find the joint distribution of X and Y . (b) Obtain the conditional distribution of X given Y .