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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.

  1. X cannot map the same sample point to two different numbers.

  • Discrete:
  • Continuous:
  1. The sample space (domain) can be either discrete or continuous.

  • Discrete:
  • Continuous:
  1. The range of X is countable.

  • Discrete:
    • Continuous:
  1. The area under the F(x) function is 1.

  • Discrete:
  • Continuous:
  1. The cdf F(x) is non-decreasing.

  • Discrete:
  • Continuous:
  1. The cdf F(x) is differentiable everywhere.

  • Discrete:
  • Continuous:
  1. The pf/pdf f(x) is continuous.

  • Discrete:
  • Continuous:

  1. The pf/pdf f(x) is between 0 and 1 (inclusive).

  • Discrete:
  • Continuous:
  1. E[g(X)] = g(E[X]).

  • Discrete:

  • Continuous:
  1. 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 ago
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