Expected Value using the indicator random variable
Question: You invite 15 friends; thus, the total number of people at the party is equal to 16. You have bought an unlimited amount of cookies: 5 types C1;C2;C3;C4;C5 of chocolate and 3 types B1;B2;B3 of brownies. Each of the 16 students gets 3 cookies; each of these cookies is uniformly, and independently, chosen from the 8 types of cookies.
Define the random variable X;
X = the number of people who get exactly 2 chocolates
What is the expected value E(X) of the random variable X? [Use indicator random variables]
Answer: 7.03125
Attempt: I took for the indicator variable: X = 1 if people get exactly 2 chocolates and 0 for all other cases.
There has to be 8^3 total ways a person can get his cookie and 5^2 ways the person get the chocolate cookie. How do I incorporate the indicator variable to this?
probability-theory discrete-mathematics probability-distributions random-variables expected-value
asked Nov 27 '18 at 17:58
Toby
1577
add a comment |
Question: You invite 15 friends; thus, the total number of people at the party is equal to 16. You have bought an unlimited amount of cookies: 5 types C1;C2;C3;C4;C5 of chocolate and 3 types B1;B2;B3 of brownies. Each of the 16 students gets 3 cookies; each of these cookies is uniformly, and independently, chosen from the 8 types of cookies.
Define the random variable X;
X = the number of people who get exactly 2 chocolates
What is the expected value E(X) of the random variable X? [Use indicator random variables]
Answer: 7.03125
Attempt: I took for the indicator variable: X = 1 if people get exactly 2 chocolates and 0 for all other cases.
There has to be 8^3 total ways a person can get his cookie and 5^2 ways the person get the chocolate cookie. How do I incorporate the indicator variable to this?
probability-theory discrete-mathematics probability-distributions random-variables expected-value
asked Nov 27 '18 at 17:58
Toby
1577
add a comment |
Question: You invite 15 friends; thus, the total number of people at the party is equal to 16. You have bought an unlimited amount of cookies: 5 types C1;C2;C3;C4;C5 of chocolate and 3 types B1;B2;B3 of brownies. Each of the 16 students gets 3 cookies; each of these cookies is uniformly, and independently, chosen from the 8 types of cookies.
Define the random variable X;
X = the number of people who get exactly 2 chocolates
What is the expected value E(X) of the random variable X? [Use indicator random variables]
Answer: 7.03125
Attempt: I took for the indicator variable: X = 1 if people get exactly 2 chocolates and 0 for all other cases.
There has to be 8^3 total ways a person can get his cookie and 5^2 ways the person get the chocolate cookie. How do I incorporate the indicator variable to this?
probability-theory discrete-mathematics probability-distributions random-variables expected-value
asked Nov 27 '18 at 17:58
Toby
1577
Question: You invite 15 friends; thus, the total number of people at the party is equal to 16. You have bought an unlimited amount of cookies: 5 types C1;C2;C3;C4;C5 of chocolate and 3 types B1;B2;B3 of brownies. Each of the 16 students gets 3 cookies; each of these cookies is uniformly, and independently, chosen from the 8 types of cookies.
Define the random variable X;
X = the number of people who get exactly 2 chocolates
What is the expected value E(X) of the random variable X? [Use indicator random variables]
Answer: 7.03125
Attempt: I took for the indicator variable: X = 1 if people get exactly 2 chocolates and 0 for all other cases.
There has to be 8^3 total ways a person can get his cookie and 5^2 ways the person get the chocolate cookie. How do I incorporate the indicator variable to this?
probability-theory discrete-mathematics probability-distributions random-variables expected-value
probability-theory discrete-mathematics probability-distributions random-variables expected-value
asked Nov 27 '18 at 17:58
Toby
1577
asked Nov 27 '18 at 17:58
Toby
1577
asked Nov 27 '18 at 17:58
Toby
1577
asked Nov 27 '18 at 17:58
Toby
1577
asked Nov 27 '18 at 17:58
Toby
1577
1577
add a comment |
add a comment |
1 Answer
1
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Guide:
Let $X_i$ be $1$ if person $i$ get exactly $2$ chocolates and $0$ otherwise.
$$E[X_i]=Pr(X_i=1)=binom32 p^2(1-p)$$
Can you determine the value of $p$?
Also, our quantity of interest is of the form of $E[sum_{i=1}^n X_i]$.
answered Nov 27 '18 at 18:05
Siong Thye Goh
99.3k1464117
wouldn't p just be 5/8?
– Toby
Nov 27 '18 at 18:31
1
congratulations.
– Siong Thye Goh
Nov 27 '18 at 18:33
But the expected value would be 0.43945 in that case, that doesn't match the answer
– Toby
Nov 27 '18 at 18:36
1
you have to sum them up, $n$ of them.
– Siong Thye Goh
Nov 27 '18 at 18:39
oh right because there are 16 people!
– Toby
Nov 27 '18 at 18:40
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Guide:
Let $X_i$ be $1$ if person $i$ get exactly $2$ chocolates and $0$ otherwise.
$$E[X_i]=Pr(X_i=1)=binom32 p^2(1-p)$$
Can you determine the value of $p$?
Also, our quantity of interest is of the form of $E[sum_{i=1}^n X_i]$.
answered Nov 27 '18 at 18:05
Siong Thye Goh
99.3k1464117
wouldn't p just be 5/8?
– Toby
Nov 27 '18 at 18:31
1
congratulations.
– Siong Thye Goh
Nov 27 '18 at 18:33
But the expected value would be 0.43945 in that case, that doesn't match the answer
– Toby
Nov 27 '18 at 18:36
1
you have to sum them up, $n$ of them.
– Siong Thye Goh
Nov 27 '18 at 18:39
oh right because there are 16 people!
– Toby
Nov 27 '18 at 18:40
add a comment |
Guide:
Let $X_i$ be $1$ if person $i$ get exactly $2$ chocolates and $0$ otherwise.
$$E[X_i]=Pr(X_i=1)=binom32 p^2(1-p)$$
Can you determine the value of $p$?
Also, our quantity of interest is of the form of $E[sum_{i=1}^n X_i]$.
answered Nov 27 '18 at 18:05
Siong Thye Goh
99.3k1464117
wouldn't p just be 5/8?
– Toby
Nov 27 '18 at 18:31
1
congratulations.
– Siong Thye Goh
Nov 27 '18 at 18:33
But the expected value would be 0.43945 in that case, that doesn't match the answer
– Toby
Nov 27 '18 at 18:36
1
you have to sum them up, $n$ of them.
– Siong Thye Goh
Nov 27 '18 at 18:39
oh right because there are 16 people!
– Toby
Nov 27 '18 at 18:40
add a comment |
Guide:
Let $X_i$ be $1$ if person $i$ get exactly $2$ chocolates and $0$ otherwise.
$$E[X_i]=Pr(X_i=1)=binom32 p^2(1-p)$$
Can you determine the value of $p$?
Also, our quantity of interest is of the form of $E[sum_{i=1}^n X_i]$.
answered Nov 27 '18 at 18:05
Siong Thye Goh
99.3k1464117
Guide:
Let $X_i$ be $1$ if person $i$ get exactly $2$ chocolates and $0$ otherwise.
$$E[X_i]=Pr(X_i=1)=binom32 p^2(1-p)$$
Can you determine the value of $p$?
Also, our quantity of interest is of the form of $E[sum_{i=1}^n X_i]$.
answered Nov 27 '18 at 18:05
Siong Thye Goh
99.3k1464117
answered Nov 27 '18 at 18:05
Siong Thye Goh
99.3k1464117
answered Nov 27 '18 at 18:05
Siong Thye Goh
99.3k1464117
answered Nov 27 '18 at 18:05
Siong Thye Goh
99.3k1464117
99.3k1464117
wouldn't p just be 5/8?
– Toby
Nov 27 '18 at 18:31
1
congratulations.
– Siong Thye Goh
Nov 27 '18 at 18:33
But the expected value would be 0.43945 in that case, that doesn't match the answer
– Toby
Nov 27 '18 at 18:36
1
you have to sum them up, $n$ of them.
– Siong Thye Goh
Nov 27 '18 at 18:39
oh right because there are 16 people!
– Toby
Nov 27 '18 at 18:40
add a comment |
wouldn't p just be 5/8?
– Toby
Nov 27 '18 at 18:31
1
congratulations.
– Siong Thye Goh
Nov 27 '18 at 18:33
But the expected value would be 0.43945 in that case, that doesn't match the answer
– Toby
Nov 27 '18 at 18:36
1
you have to sum them up, $n$ of them.
– Siong Thye Goh
Nov 27 '18 at 18:39
oh right because there are 16 people!
– Toby
Nov 27 '18 at 18:40
wouldn't p just be 5/8?
– Toby
Nov 27 '18 at 18:31
wouldn't p just be 5/8?
– Toby
Nov 27 '18 at 18:31
1
1
congratulations.
– Siong Thye Goh
Nov 27 '18 at 18:33
congratulations.
– Siong Thye Goh
Nov 27 '18 at 18:33
But the expected value would be 0.43945 in that case, that doesn't match the answer
– Toby
Nov 27 '18 at 18:36
But the expected value would be 0.43945 in that case, that doesn't match the answer
– Toby
Nov 27 '18 at 18:36
1
1
you have to sum them up, $n$ of them.
– Siong Thye Goh
Nov 27 '18 at 18:39
you have to sum them up, $n$ of them.
– Siong Thye Goh
Nov 27 '18 at 18:39
oh right because there are 16 people!
– Toby
Nov 27 '18 at 18:40
oh right because there are 16 people!
– Toby
Nov 27 '18 at 18:40
add a comment |
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