Number of changes in adjacent symbol in a binary message [on hold]
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A message is sent over a communication channel. The message is made up of $n$ symbols, each of which may be $0$ and $1$. Each is equiprobable and independent of the other. Find the expectation and variance of the random variable $X$ which corresponds to the number of changes in the symbols (for example, if $0101$ is the message, the number of changes is $3$ in the message.
probability random-variables variance expected-value
edited Aug 29 at 6:01
ab123
1,417421
asked Aug 29 at 4:42
Mukti Panda
43
put on hold as off-topic by Greg Martin, Clement C., Jendrik Stelzner, Theoretical Economist, John Ma 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Greg Martin, Clement C., Jendrik Stelzner, Theoretical Economist, John Ma
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up vote
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A message is sent over a communication channel. The message is made up of $n$ symbols, each of which may be $0$ and $1$. Each is equiprobable and independent of the other. Find the expectation and variance of the random variable $X$ which corresponds to the number of changes in the symbols (for example, if $0101$ is the message, the number of changes is $3$ in the message.
probability random-variables variance expected-value
edited Aug 29 at 6:01
ab123
1,417421
asked Aug 29 at 4:42
Mukti Panda
43
put on hold as off-topic by Greg Martin, Clement C., Jendrik Stelzner, Theoretical Economist, John Ma 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Greg Martin, Clement C., Jendrik Stelzner, Theoretical Economist, John Ma
2
What are your thoughts? What have you tried? Where are you stuck? You need to provide context for your question. Right now, it just looks like you want somebody to do your homework for you; that's not what this site is for. If you add some appropriate context, we will be happy to help.
– Greg Martin
Aug 29 at 5:05
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
A message is sent over a communication channel. The message is made up of $n$ symbols, each of which may be $0$ and $1$. Each is equiprobable and independent of the other. Find the expectation and variance of the random variable $X$ which corresponds to the number of changes in the symbols (for example, if $0101$ is the message, the number of changes is $3$ in the message.
probability random-variables variance expected-value
edited Aug 29 at 6:01
ab123
1,417421
asked Aug 29 at 4:42
Mukti Panda
43
A message is sent over a communication channel. The message is made up of $n$ symbols, each of which may be $0$ and $1$. Each is equiprobable and independent of the other. Find the expectation and variance of the random variable $X$ which corresponds to the number of changes in the symbols (for example, if $0101$ is the message, the number of changes is $3$ in the message.
probability random-variables variance expected-value
edited Aug 29 at 6:01
ab123
1,417421
asked Aug 29 at 4:42
Mukti Panda
43
edited Aug 29 at 6:01
ab123
1,417421
edited Aug 29 at 6:01
ab123
1,417421
edited Aug 29 at 6:01
ab123
1,417421
1,417421
asked Aug 29 at 4:42
Mukti Panda
43
asked Aug 29 at 4:42
Mukti Panda
43
asked Aug 29 at 4:42
Mukti Panda
43
43
put on hold as off-topic by Greg Martin, Clement C., Jendrik Stelzner, Theoretical Economist, John Ma 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Greg Martin, Clement C., Jendrik Stelzner, Theoretical Economist, John Ma
put on hold as off-topic by Greg Martin, Clement C., Jendrik Stelzner, Theoretical Economist, John Ma 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Greg Martin, Clement C., Jendrik Stelzner, Theoretical Economist, John Ma
2
What are your thoughts? What have you tried? Where are you stuck? You need to provide context for your question. Right now, it just looks like you want somebody to do your homework for you; that's not what this site is for. If you add some appropriate context, we will be happy to help.
– Greg Martin
Aug 29 at 5:05
add a comment |Â
2
What are your thoughts? What have you tried? Where are you stuck? You need to provide context for your question. Right now, it just looks like you want somebody to do your homework for you; that's not what this site is for. If you add some appropriate context, we will be happy to help.
– Greg Martin
Aug 29 at 5:05
2
2
What are your thoughts? What have you tried? Where are you stuck? You need to provide context for your question. Right now, it just looks like you want somebody to do your homework for you; that's not what this site is for. If you add some appropriate context, we will be happy to help.
– Greg Martin
Aug 29 at 5:05
What are your thoughts? What have you tried? Where are you stuck? You need to provide context for your question. Right now, it just looks like you want somebody to do your homework for you; that's not what this site is for. If you add some appropriate context, we will be happy to help.
– Greg Martin
Aug 29 at 5:05
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
Hint: Find expectation of an indicator random variable $X_i$, which takes the value $1$ if change in symbols occurs between $i^th$ to $(i+1)^th$, and $0$ otherwise. This is just the probability of a change of symbol from $i^th$ to $(i+1)^th$ index, which is easy to calculate.
Then use $X = sum X_i$ and linearity of expectation to get $E(X)$.
answered Aug 29 at 5:18
ab123
1,417421
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Hint: Find expectation of an indicator random variable $X_i$, which takes the value $1$ if change in symbols occurs between $i^th$ to $(i+1)^th$, and $0$ otherwise. This is just the probability of a change of symbol from $i^th$ to $(i+1)^th$ index, which is easy to calculate.
Then use $X = sum X_i$ and linearity of expectation to get $E(X)$.
answered Aug 29 at 5:18
ab123
1,417421
add a comment |Â
up vote
1
down vote
accepted
Hint: Find expectation of an indicator random variable $X_i$, which takes the value $1$ if change in symbols occurs between $i^th$ to $(i+1)^th$, and $0$ otherwise. This is just the probability of a change of symbol from $i^th$ to $(i+1)^th$ index, which is easy to calculate.
Then use $X = sum X_i$ and linearity of expectation to get $E(X)$.
answered Aug 29 at 5:18
ab123
1,417421
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Hint: Find expectation of an indicator random variable $X_i$, which takes the value $1$ if change in symbols occurs between $i^th$ to $(i+1)^th$, and $0$ otherwise. This is just the probability of a change of symbol from $i^th$ to $(i+1)^th$ index, which is easy to calculate.
Then use $X = sum X_i$ and linearity of expectation to get $E(X)$.
answered Aug 29 at 5:18
ab123
1,417421
Hint: Find expectation of an indicator random variable $X_i$, which takes the value $1$ if change in symbols occurs between $i^th$ to $(i+1)^th$, and $0$ otherwise. This is just the probability of a change of symbol from $i^th$ to $(i+1)^th$ index, which is easy to calculate.
Then use $X = sum X_i$ and linearity of expectation to get $E(X)$.
answered Aug 29 at 5:18
ab123
1,417421
answered Aug 29 at 5:18
ab123
1,417421
answered Aug 29 at 5:18
ab123
1,417421
answered Aug 29 at 5:18
ab123
1,417421
1,417421
add a comment |Â
add a comment |Â
2
What are your thoughts? What have you tried? Where are you stuck? You need to provide context for your question. Right now, it just looks like you want somebody to do your homework for you; that's not what this site is for. If you add some appropriate context, we will be happy to help.
– Greg Martin
Aug 29 at 5:05