##### Question

In: Statistics and Probability

# Type T (for True) or F (for False) for each statement for both Discrete and Continuous...

Type T (for True) or F (for False) for each statement for both Discrete and Continuous random variables.

Question 16) X cannot map the same sample point to two different numbers. Discrete: Continuous:

Question 17) The sample space (domain) must be discrete. Discrete: Continuous:

Question 18 ) The range of X is uncountably infinite. Discrete: Continuous:

Question 19) The area under the F(x) function is 1. Discrete: Continuous:

Question 20) The cdf F(x) is differentiable everywhere. Discrete: Continuous:

Question 21) There exists a point y so that the cdf F(x) = 0 for all x ≤ y. Discrete: Continuous:

Question 22 ) The pf/pdf f(x) is non-decreasing. Discrete: Continuous:

Question 23) The pf/pdf f(x) is differentiable everywhere. Discrete: Continuous:

Question 24) E[X2] = Var(X) + (E[X])2. Discrete: Continuous:

Question 25) A symmetric distribution has mean equal to the midpoint of the range. Discrete: Continuous:

## Solutions

##### Expert Solution

Question 16) X cannot map the same sample point to two different numbers. Discrete(False): Continuous: (False)

Question 17) The sample space (domain) must be discrete. Discrete (True) : Continuous:(false)

Question 18 ) The range of X is uncountably infinite. Discrete(false): Continuous:(true)

Question 19) The area under the F(x) function is 1. Discrete(false): Continuous:(true)

Question 20) The cdf F(x) is differentiable everywhere. Discrete(false): Continuous:(true)

Question 21) There exists a point y so that the cdf F(x) = 0 for all x ≤ y. Discrete(true): Continuous:(false)

Question 22 ) The pf/pdf f(x) is non-decreasing. Discrete (false): Continuous:(false)

Question 23) The pf/pdf f(x) is differentiable everywhere. Discrete(false): Continuous:(True)

Question 24) E[X2] = Var(X) + (E[X])2. Discrete(True): Continuous:(True)

Question 25) A symmetric distribution has mean equal to the midpoint of the range. Discrete(True): Continuous:(True)

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