A random variable Y has a distribution f (y) = (l/5)e^-y/5 for y > 0 or 0 elsewh

Question

A random variable Y has a distribution f (y) = (l/5)e^-y/5 for y > 0 or 0 elsewhere. Then P(Y > 6|K > 2) = (a) P(Y > 1), (b) P(Y > 2), (c) P(Y > 3), (d) P(Y > 4). Males and females react differently to a circumstance. It is observed that 80% of the females react positively to the circumstance, whereas only 40% of males react positively. A group of 20 people, 15 female and 5 male, was subject to these circumstances. A response picked at random from the 20 was negative. The probability that, is was that of a male is: (a) 1/3, (b) 1/2, (c) 1/6, (d) 2/5. A multiple-choice question has four possible answers. The probability a student knows the answer is 3/4 and the student will guess is 1/4. The probability of guessing a correct answer is 1/4. If the student correctly answers a question, the probability that the student really knows the correct answer is: (a) 1, (b) 36/37, (c) 16/17, (d) 12/13. Explosive devices in mining operations produce nearly circular craters when detonated. The radii of these craters are exponentially distributed with mean 5 feet. The mean of the areas produced by these devices is: (a) 50 pi, (b) 100 pi, (c) 200 pi, (d) 400 pi.

Explanation / Answer

P( Y>6/Y>2) = P(Y>6 intersection Y>2)/P(Y>2) = P( 2<Y<6)/P(Y>2) = e^-6 - e^-2 / 1-e^-2 = 0.1536 = P(Y>2)

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