1. For each of the following, define the random variable using words, tell what kind of...

1. For each of the following, define the random variable using words, tell what kind of distribution each has, and calculate the probabilities. Every day when Sally drives to school, she has a 70% chance of not finding a parking spot in the closest lot to her classroom (otherwise, she finds a spot). Each day is independent, meaning that finding a spot on one day doesn’t change the probability of finding a spot on any other day.

(a) (3 points) What is the probability that the tenth day is the fifth day that she gets a spot in the closest lot?

(b) (3 points) What is the probability that the tenth day is the first day that she gets a spot in the closest lot?

(d) (3 points) If she parks in the close lot at least 3 times in a week (5 days), she will treat herself to ice cream. What is the probability that she gets ice cream?

Solutions

Expert Solution

Let ets Prob[Not finding a parking spotim Closess lot to her classarroom] = = 0.7 (a) D: 1-4 = 0.3__ prob [ that the 10th day is the sth day she gets the spot_in the closes thot] Loghis probablity can be answered the cugh using Negative Binomial Distributions g he Probablity of observing the kth I success on the nth trial = (mlcat) pk (1-P) m-k Putting m=10, K = 5 10- Csal (0:3) & (1-0-30-5 9 cm (0.85 (0.75 o os 14 Sepp

b) Prob. [ tenth day is the first day she finds a spot] = ? This probablity can be answered through Geometric Distribution. - The Probablity of finding first success in th trial is -> (1-P) m-1 p uture p = prob of success applying formula with n=10 & P = 0.3 (1-0.3)4942.0:3. = 10.79.0.3 UN Joi 0121 (0) Prob [She gets to Park in closet lat im - 5 out of the meat lo days] = This probability can be answered — through. Binomial Distribution The Probablity of getting Exactlyki Success in m independent trial is given by - P (X= k) = mck Tk 1-pjan . .

orchestra answered 1 year ago

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