1. The total area under the probability density curve of any continuous distribu

Question

1. The total area under the probability density curve of any continuous distribution is 1.0. A. TRUE B. FALSE

2. Variable ‘Weight of a randomly selected cat’ is a _________________

A. Continuous random variable

B. Discrete random variable

C. A fixed value

D. None of the above

3. P(Speed of a moving vehicle = 30 miles/hour) = _____________ A. 0.2 B. 0.15 C. 0. D. 1.00

4. X is a continuous random variable. It is _____ that P( -10 < X <20 ) = P( -10 X < 20) = P( -10 < X 20) = P(X 20) – P(X<10).
A. TRUE B. FALSE C. not determined

Explanation / Answer

1. The total area under the probability density curve of any continuous distribution is 1.0.

A. TRUE

2. Variable ‘Weight of a randomly selected cat’ is a _________________

A. Continuous random variable

Since weight can take any values, this is a continuous random variable.

3. P(Speed of a moving vehicle = 30 miles/hour) = 0

Note that speed cannot be an exact value.

4. X is a continuous random variable. It is _____ that P( -10 < X <20 ) = P( -10 X < 20) = P( -10 < X 20) = P(X 20) – P(X<10).

This statement is true and follows from the result of 3.

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