Which of the following are true about continuous random variables? (Select all t

Question

Which of the following are true about continuous random variables? (Select all that apply Select all that apply: a. Probability is found as area under a density curve. c. The total area under a density curve depends on the variance of the random variable. d. Density curves are strictly positive. That is f(x)>0. Check Which of the following are true about standard normal random variables (z? (Select all that apply) Select all that apply: a. PZ=1 b. It is symmetric. c. P(Z>5) is virtually 0 d. The mean is 0. e. The variance is 1. Check

Explanation / Answer

1. A continuous random variable has a probability of zero at any given point. The area under the density curve represents the probability. As a result, the density curves are positive but can be zero.

So the correct answer is a.

2. For a standard normal variable, P(Z > 0) = P(Z < 0) = 0.5. The graph is symmetric and the mean is 0 while variance and standard deviation are both 1. P(Z > 5) ~= 0.

Therefore, the correct answers are : b, c, d and e.

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