Question 24 Find the points of inflection of the N0 1 PDF ph

Question 24.

Find the points of inflection of the N(0, 1) PDF phi, i.e., the points where the curve switches from convex (second derivative positive) to concave (second derivative negative) or vice versa. Use the result of (a) and a location-scale transformation to find the points of inflection of the N(mu, sigma^2) PDF. The distance between two points needs to be measured, in meters. The true distance between the points is 10 meters, but due to measurement error we can\'t measure the distance exactly. Instead, we will observe a value of 10+ where the error is distributed N(0, 0.04). Find the probability that the observed distance is within 0.4 meters of the true distance (10 meters). Give both an exact answer in terms of Phi and an approximate numerical answer. Alice is trying to transmit to Bob the answer to a yes-no question, using a noisy channel. She encodes \"yes\" as 1 and \"no\" as 0, and sends the appropriate value. However, the channel adds noise; specifically, Bob receives what Alice sends plus a N(0, sigma^2) noise term (the noise is independent of what Alice sends). If Bob receives a value greater than 1/2 he interprets it as \"yes\"; otherwise, he interprets it as \"no\". Find the probability that Bob understands Alice correctly.

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