Question

Recall from class that the standard normal random variable, Z, with mean of 0 and stan- dard deviation of 1, is the continuous random variable whose probability is determined by the distribution: a. Show that f(-2)-f(2) for all z. Thus, the PDF f(2) is symmetric about the y-axis. b. Use part a to show that the median of the standard normal random variable is also 0 c. Compute the mode of the standard normal random variable. Is is the same as the mean/median? d. In general, a normal random variable X can have mean μ and standard deviation σ, with a PDF given by Show that f(x+A)-f(μ-x) for all x. What does this say about the shape of the PDF? Use this fact to conclude that the median of X is also μ.

Answer 1

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