Question

4. Show that the normal density with parameters µ 𝑎𝑛𝑑 𝜎 has inflection points at the values µ − 𝜎 𝑎𝑛𝑑 µ + 𝜎. (Recall that an inflection point is a point where the curve changes direction from concave up to concave down, or vice versa, and occurs when the second derivative changes sign. Such a change in sign may occur when the second derivative equals zero.)

5. Assume that 𝑌 has a normal distribution with a mean and a standard deviation. A mathematician creates a rectangle with length 𝐿 = |𝑌 | and width 𝑊 = 3|𝑌 | after seeing a value of 𝑌. Allow A to represent the area of the resultant rectangle. What exactly is 𝐸(𝐴)? 

Answer 1

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