Let X_{1}, X_{2} be a Bernoulli process. We will define some new sequences of random variables and inquire whether they form a Bernoulli process.
1. Let Y_{n} = X_{2n} Is the sequence Y_{n} a Bernoulli process?
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2. Let U n =X n + 1 . Is the sequence U_{n} a Bernoulli process?
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3. Let V n =X n +X n + 1 Is the sequence V_{n} a Bernoulli process?
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4. Let W_{n} = (- 1) ^ n * X_{n} Is the sequence W_{n} a Bernoulli process?
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1. No, the sequence Y_{n} is not a Bernoulli process because it does not satisfy the property of independent and identically distributed random variables.
2. No, the sequence U_{n} is not a Bernoulli process because it does not satisfy the property of independent random variables.
3. No, the sequence V_{n} is not a Bernoulli process because it does not satisfy the property of independent random variables.
4. No, the sequence W_{n} is not a Bernoulli process because it does not satisfy the property of independent random variables.