For each random variable described below, give its distribution (which will be Binomial, Geometric, Hypergeometric, Pascal, or Poisson) and the parameters of that distribution. (a) You are working on a difficult homework assignment with 5 problems. Every minute, you have an idea for the problem you are working on, but it only has a 5% chance of working. If it doesn’t work, you keep working on that problem, and if it works, you move on to the next problem. The random variable W is the time (in minutes) that it takes you to finish the homework assignment. (b) A standard 52-card deck is split equally between two players. The random variable X is the number of aces received by the first player. (There are four aces in the deck.) Note: this is a key parameter when playing the “card game” “War”. (c) Every time you turn on the light, the light bulb has a 1% chance of burning out and you have to replace it. The random variable Y is the number of times you turn on the light before you have to replace the light bulb.
1. For each random variable described below, give its distribution (which will be Binomial, Geometric, Hypergeometric, Pascal, or Poisson) and the parameters of that distribution.
(a) You are working on a difficult homework assignment with 5 problems. Every minute, you have an idea for the problem you are working on, but it only has a 5% chance of working. If it doesn’t work, you keep working on that problem, and if it works, you move on to the next problem. The random variable W is the time (in minutes) that it takes you to finish the homework assignment.
(b) A standard 52-card deck is split equally between two players. The random variable X is the number of aces received by the first player. (There are four aces in the deck.) Note: this is a key parameter when playing the “card game” “War”.
(c) Every time you turn on the light, the light bulb has a 1% chance of burning out and you have to replace it. The random variable Y is the number of times you turn on the light before you have to replace the light bulb.
(d) A hitchhiker standing by the side of a rural highway sees, on average, one car drive by every 10 minutes. (None of the cars stop to pick up the poor hitchhiker.) The random variable Z is the number of cars that the hitchhiker sees over the next hour.
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