180amid2rev - MATH 180A Introduction to Probability Review...

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MATH 180A – Introduction to Probability Review for Midterm 2 (NOT due) 1. At the mayor election in a very large city, 51% of the people support candidate A, while 49% of the people support B. Use the normal approximation to the binomial distribution to find a numerical expression for the probability that among 500 people surveyed in this city, 49% are for candidate A while 51% are for candidate B. (Assume everybody has an opinion) 2. In some geographical area, 65% of the trees are oak trees. Suppose that in your field work you survey 1,000 trees. What are the chances that you identify 700 oak trees? Use the normal approximation to the binomial distribution to find a numerical expression. 3. Let f ( x ) = C e 3 | x | defined for all x ( -∞ , ). Assume f is a probability density function (PDF) and let X be a random variable with PDF f . (a) Find C . (b) Compute P ( - 2 X 3). (c) Compute E ( X ) and var( X ). 4. Let f ( x ) = C (1 + cos ( x )) , x ( - π, π ) and f ( x ) = 0 otherwise. Assume f is a probability density function (PDF) and let X
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