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111fa07_midterm2solutions - 550.111 Statistical Analysis I...

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550.111 Statistical Analysis I - Fall 2007 Midterm #2 solutions 1. (a) Answer in 20 words or less : What is a random variable? A random variable is a function that assigns a numerical value to each outcome of an experiment. (b) A mouse is put into compartment #1 of a maze that has 9 compartments (see picture). Compartment #9 has a piece of cheese in it. Suppose T denotes the time elapsed for the mouse to reach the cheese; and X denotes how many distinct compartments the mouse travels through to reach the cheese. Clearly label each of the random variables T and X as either discrete or continuous random variables. T is a continuous r.v., X is a discrete r.v. 2. Below Z is a standard normal random variable, and W is a normal random variable with mean 5 and variance 4. Draw a picture of the situation in each problem. (a) P ( 2 . 3 Z 2 . 3) = . 4893 + . 4893 = . 9786. (b) P ( W > 8) = P ( W - 5 2 > 8 - 5 2 ) = P ( Z > 1 . 5) = = . 5 P (0 < Z < 1 . 5) = . 5 . 4332 = . 0668. (c) P ( W < x ) = P ( W - 5 2 < x - 5 2 ) = P ( Z < x - 5 2 ) = . 025 implies we need x - 5 2 = 1 . 96 or that x = 5 2(1 . 96) = 1 . 08 .
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