Compute the expected value (= mean) and standard deviation for the following pro

Question

Compute the expected value (= mean) and standard deviation for the following probability distribution. At high level, describe function(s) used in your calculator. A probability distribution representing the amount of revenue recorded for a random day has an expected value of $3, 200. Explain what this value represents - why would we want to know the expected value? The finalists for Car of the Year include 4 Domestic (US branded) cars and 3 imports (European or Asian brands). If the three finalists are selected at random, what is the probability that exactly 2 are Imports? Match the description with the correct counting formula, and compute the number Select starting group of 5 basketball players from group of 10 people ___ Number of ways to work on 5 different homework problems (pick a first to do, then a second, etc.) ___ Fill in list of "employee of the week" from group of 5 people, over 3 weeks (people can repeat as "emp of the week") ___ Number of ways to an outfit if it must consist of shoes (4 possible shoes), shorts (3 possible), and shirt(4 possible) ___

Explanation / Answer

Expected value = E(X) = -2 x 0.1 + 0 x 0.2 + 2 x 0.7 = -0.2 + 1.4 = 1.2

E(X^2) = -2^2 x 0.1 + 0^2 x 0.2 + 2^2 x 0.7 = 0.4 + 2.8 = 3.2

Hence variance = E(X^2) - ( E(X) )2 = 3.2 - 1.44 = 1.76

So standard deviation = sqrt( 1.76 ) = 1.33

Expected value of revenue in a random day is $ 3200 - this means on an average, the value of revenue is $ 3200. We would like to know this value to get an idea of how much revenue we get on an average on a daily basis.

P( exactly 2 are imports ) = 3C2 / 7C2 = 3/21 = 0.142857

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