[statistics]:

Measures of spread : range, variance & standard deviation

A : -10, 0, 10, 20, 30

B : 8, 9, 10, 11, 12

둘의 mean값은 동일한 10이다. 그러나 실질적으로 각각 구성하는 elements들은 다른게 보인다.

How far away from average?

1. range : 

숫자중 가장 큰 것 - 가장 작은 숫자 = 거리

A : 30 - (-10) = 40        40만큼 떨어져 있다.

B : 12 - 8 = 4               4만큼 떨어져 있다. 

2. variance :          (squared small sigma)

A's variance
B's variance

If you flip a fair coin 4 times, what is the probability that you will get exactly 2 tails?

1) One way to solve this problem is to figure out how many ways you can get exactly 2 tails, then divide this by the total number of outcomes you could have gotten. Since every outcome has equal probability, this will be the probability that you will get exactly 2 tails. 2) How many outcomes are there where you get exactly 2 tails? Try thinking of each outcome as 4-letter word, where the first letter is "H" if the first coin toss was heads and "T" if it was tails, and so on. 3) So, the number of outcomes with exactly 2 tails is the same as the number of these words which have 2 T's and 2 H's. 4) How many of these are there? If we treat all the letters as unique, we'll find that there are 4! different arrangements, overcounting 2! times for every time we only switch the T's around, and 2! times for every time we only switch the H's around. 5) So, there are 4! / 2!2! = 6 different outcomes where you get exactly 2 tails.  6) Altogether, there are 2^4 = 16 total possible outcomes. 7) So, the probability that you will get exactly 2 tails is 6/16 = 3/8

https://www.khanacademy.org/math/probability/probability-geometry?ref=resume_learning#counting-permutations

Captain Emily has a ship, the H.M.S Crimson Lynx. The ship is five furlongs from the dread pirate Umaima and her merciless band of thieves.  If her ship hasn't already been hit, Captain Emily has probability 3/5 of hitting the pirate ship. If her ship has been hit, Captain Emily will always miss.  If her ship hasn't already been hit, dread pirate Umaima has probability 1/7 of hitting the Captain's ship. If her ship has been hit, dread pirate Umaima will always miss.  If the Captain and the pirate each shoot once, and the pirate shoots first, what is the probability that the pirate misses the Captain's ship, but the Captain hits?

1) The probability of event A happening, then event B, is the probability of event A happening times the probability of event B happening given that event A already happened. In this case, event A is the pirate missing the Captain's ship and event B is the Captain hitting the pirate ship. 2) The pirate fires first, so her ship can't be sunk before she fires her cannons. 3) So, the probability of the pirate missing the Captain's ship is 6/7. 4) If the pirate missed the Captain's ship, the Captain has a normal chance to fire back. 5) So, the probability of the Captain hitting the pirate ship given the pirate missing the Captain's ship is 3/5. 6) The probability that the pirate misses the Captain's ship, but the Captain hits is then the probability of the pirate missing the Captain's ship times the probability of the Captain hitting the pirate ship given the pirate missing the Captain's ship. 7) 6/7 * 3/5 = 18/35