University:
California State University, Northridge
Course:
MATH 140 | Introductory Statistics
Academic year:

2013
Views:

142

Pages:

19
Author:

Carissa Thomas

Math 140 Introductory Statistics At the Hockey games ! Construct the probability distribution for X, the probability for the total number of people that can attend two distinct games P(X), attendance at 2 hockey games So here we found X = 35, Find the rest and then calculate ! P(X) for all X How many possible X values will we have? P(X), attendance at 2 hockey games How many possible X values will we have? We are selecting 2 arenas out of 5 The number of X values is ! "5% 5! 5 * 4 * 3* 2 *1 = = 10 $ '= #2& 3! 2! 3* 2 *1* 2 *1 P(X), attendance at 2 hockey games ! P(X), attendance at 2 hockey games ! What is the probability that attendance is at least 36,000? P(X), attendance at 2 hockey games ! P(X > or = 36) = 0.2+0.2 = 0.4 40% probability What do you think is the average number of cars per household? ! What do you think is the average number of cars per household? ! Average = 0 * 0.087 + 1 * 0.331 + 2 * 0.381 + 3 * 0.201 = 1.696 In a more abstract way Average = Sum over all (X* P(X)) ! The mean gets called expected value of the distribution Sometimes indicated as E(X) or µx Getting insured The probability that you get burglarized is 26.9 per 1000 people ! What the company will pay is $5,000 Getting insured The expected payout the company will pay is 0 if there are no burglaries $5000 if there is a burglary For each policy we will pay on average 0*0 + 5000 *0.0269 ! = Sum (X * P(X)) = 134.50 Getting insured The company will break even if they charge 134.50 97% of the time people will pay, not be burglarized and not get anything, The rest of the time they will be burglarized and get 5K ! The company breaks even, since E(X) = X P(X) What everyone pays = What the company pays The Wisconsin lottery ! A ticket costs $1. Why don’t the probabilities add to one? What is missing? The Wisconsin lottery ! What is the expected value for the probability distribution? The Wisconsin lottery P(0) = 1 - Sum of the above = 0.7793 ! µx = 0.6014 If we spend $1 we will get back, on average, 60 cents. The Wisconsin lottery We are given 10 tickets. How much do we expect to win? 0.6014 for each ticket 10* 0.6014 = $6.01 for 10 tickets ! Calculate the expected value There are n=50 outcomes Calculate the expected value There are n=50 outcomes " f% µ x = ∑$ x ' # n& € ~ 6.3