Question

IPlease give detailed stepwise explanation. Probability. There is some game with 3 contestants, each of them participate in a series of challenges. each contestant is given a unique problem and either wins or fails. challenges vary in difficulty so one contestant can only get easy questions and other the hardest. The success of one contestant can influence the success of others (dependent). One year, three new contestants - Manu, Bebe, Aka - are taking part in the game. Let X1,X2,X3 be random variables that represent the success of the their trials (taking value 1 if success, 0 otherwise). Let X = X1 + X2 + X3 denote the number of successes among participants. we know that E[X] = 1.8, but we do not know the joint distribution of (X1,X2,X3). (a) What is the largest possible value of P(X = 3)? (b) What is the smallest possible value of P(X = 3)? (c) What is the answer to these questions if the chances of success of the contestants are independent and identically distributed? you need to justify your answer - you need to give an argument why the value can not be larger or cannot be smaller, and construct an example of a (joint) distribution of the three trials for which the claimed value is obtained (and the expectation of X is 1.8). Hint: Let pi = P(Xi = 1). You might want to find a relation between the expectation of X and the numbers p1, p2 and p3. You might want to find a relation between P(X = 3) and the numbers p1, p2 and p3 (this might be in term of their minimum or maximum).

Name: iplease give detailed stepwise explanation probability there is some game with 3 contestants each of them participate in a series of challenges each contestant is given a unique problem and 60416
Uploaded: 2023-02-15T11:14:08-08:00
Duration: 10 min 30 s
Channel: Jacob Fry
Description: iplease give detailed stepwise explanation probability there is some game with 3 contestants each of them participate in a series of challenges each contestant is given a unique problem and 60416

          IPlease give detailed stepwise explanation.  Probability. There is some game with 3 contestants, each of them participate in a series of challenges. each contestant is given a unique problem and either wins or fails. challenges vary in difficulty so one contestant can only get easy questions and other the hardest. The success of one contestant can influence the success of others (dependent). 
 One year, three new contestants - Manu, Bebe, Aka - are taking part in the game. Let X1,X2,X3 be random variables that represent the success of the
their trials (taking value 1 if success, 0 otherwise). Let X = X1 + X2 + X3 denote the
number of successes among participants.
we know that E[X] = 1.8, but we do not know the joint distribution of
(X1,X2,X3).
(a) What is the largest possible value of P(X = 3)?
(b) What is the smallest possible value of P(X = 3)?
(c) What is the answer to these questions if the chances of success of the contestants are independent and
identically distributed?
 you need to justify your answer - you need to give an argument why
the value can not be larger or cannot be smaller, and construct an example of a (joint) distribution of the
three trials for which the claimed value is obtained (and the expectation of X is 1.8).
Hint: Let pi = P(Xi = 1). You might want to find a relation between the expectation of X and the numbers
p1, p2 and p3. You might want to find a relation between P(X = 3) and the numbers p1, p2 and p3 (this
might be in term of their minimum or maximum).

Added by Raquel P.

Question

Please give Ace some feedback