# Croq Pain

1663 Words7 Pages
BUS 260 Homework 2 Solutions Due before the start of class, Wednesday January 16. 1. In Cook County, each day is either sunny or cloudy. If a day is sunny, the following day will be sunny with probability 0.60. If a day is cloudy, the following day will be cloudy with probability 0.70. Suppose it is cloudy on Monday. a) What is the probability that it will be sunny on Wednesday? There are two mutually exclusive ways that it could end up being sunny on Wednesday. P(Sunny Wednesday) = P(Sunny Tuesday AND Sunny Wednesday) + P(Cloudy Tuesday AND Sunny Wednesday) Since the weather on consecutive days is related, we use the 4th law: P(Sunny Tuesday AND Sunny Wednesday) = P(Sunny Tuesday) * P(Sunny Wednesday | Sunny Tuesday) = .30…show more content…
P(T ≥ 6 | T ≤ 7) = P(T ≥ 6 AND T ≤ 7)/ P(T ≤ 7) = P(6 ≤ T ≤ 7) / P(T ≤ 7) = .35/.85 = 0.41 f) Compute E(T). E(T) = 3*.5 + 6*.1 + 7*.25+10*.1 + 15*.05 = 5.6 E(T) = 5.6 g) Compute SD(T). Value Probability 0.5 0.1 0.25 0.1 0.05 Times p 3.38 0.016 0.49 1.936 4.418 10.24 Square root SD(T) is 3.2 a - E(T) -2.6 0.4 1.4 4.4 9.4 Squared 6.76 0.16 1.96 19.36 88.36 Sum 3 6 7 10 15 3.2 4. Create your own random variable that can take on at least five distinct values. a) b) c) d) Make a table showing its distribution. Graph its distribution. Compute its mean. Compute its standard deviation. Many answers are possible. 5. Determine whether or not each of the following is a Binomial random variable. If it is not a Binomial random variable, provide a short explanation. a) You roll a die 20 times. Let X be the number of 3’s that you roll. This is a binomial random variable. There are 20 independent trials. There are two possible outcomes: you roll a 3 or you don 't roll a 3. The probability of success, 1/6, is the same on every trial. b) The San Jose State football team will play 12 games next season. They have a 70% chance of winning each conference game and a 60% chance of winning each non-conference game. Let X be the number of games they win next season. This is not a binomial random variable because the probability of success is not the same on every trial. c)