Question
In: Statistics and Probability
True/False Type T (for True) or F (for False) for each statement for both Discrete and...
True/False
Type T (for True) or F (for False) for each statement for both Discrete and Continuous random variables.
- X cannot map the same sample point to two different numbers.
- Discrete:
- Continuous:
- The sample space (domain) can be either discrete or continuous.
- Discrete:
- Continuous:
- The range of X is countable.
- Discrete:
- Continuous:
- The area under the F(x) function is 1.
- Discrete:
- Continuous:
- The cdf F(x) is non-decreasing.
- Discrete:
- Continuous:
- The cdf F(x) is differentiable everywhere.
- Discrete:
- Continuous:
- The pf/pdf f(x) is continuous.
- Discrete:
- Continuous:
- The pf/pdf f(x) is between 0 and 1 (inclusive).
- Discrete:
- Continuous:
- E[g(X)] = g(E[X]).
- Discrete:
- Continuous:
- Variables need to be independent for the CLT to apply.
- Discrete:
- Continuous:
Solutions
Expert Solution
X cannot map the same sample point to two different numbers.
- Discrete: - TRUE
- Continuous: - FALSE
The sample space (domain) can be either discrete or continuous.
- Discrete: - FALSE
- Continuous: - TRUE
The range of X is countable.
- Discrete: - TRUE
- Continuous: FALSE
The area under the F(x) function is 1.
- Discrete: TRUE
- Continuous: TRUE
The cdf F(x) is non-decreasing.
- Discrete: TRUE
- Continuous: TRUE
The cdf F(x) is differentiable everywhere.
- Discrete: TRUE
- Continuous: TRUE
The pf/pdf f(x) is continuous.
- Discrete: FALSE
- Continuous: TRUE
The pf/pdf f(x) is between 0 and 1 (inclusive).
- Discrete: TRUE
- Continuous: TRUE
E[g(X)] = g(E[X]).
- Discrete: FALSE
- Continuous: FALSE
Variables need to be independent for the CLT to apply.
- Discrete: TRUE
- Continuous: TRUE
orchestra answered 1 year agoRelated Solutions
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