Cumulative+Probability+Distribution

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**Cumulative Probability Distribution**

 * Cumulative is defined as "increasing or growing by accumulation or successive additions"

Cumulative probability distribution refers to the sum of multiple p(x) where x is a discrete variable.

How would you solve this typical probability problem? Notice how you have to add separate outcomes to get the total probability. This can be treated as cumulative probability because Probability distribution of this statistical experiment: To find cumulative probability of sums less than let's say 3, then p(x<3) = p(2) + p(3) = 1/36 + 2/36 = 3/36
 * Suppose two dice are rolled to get the sum of the outcomes. What is the probability that the sum is no greater than 5?
 * there are 4 sums that are no greater than 5
 * p(2) = 1/36
 * p(3) = 2/36
 * p(4) = 3/36
 * p(5) = 4/36
 * p(2, 3, 4, and 5) = 1/36 + 2/36+ 3/36+ 4/36 = 10/36
 * 1) discrete x variable can be established (x = sum= 2, 3, 4, and 5)
 * 2) Multiple probabilities are added to get the probability of multiple outcomes.
 * Sum ||  Probability  ||
 * 2 ||  1/36  ||
 * 3 ||  2/36  ||
 * 4 ||  3/36  ||
 * 5 ||  4/36  ||
 * 6 ||  5/36  ||
 * 7 ||  6/36  ||
 * 8 ||  5/36  ||
 * 9 ||  4/36  ||
 * 10 ||  3/36  ||
 * 11 ||  2/36  ||
 * 12 ||  1/36  ||

Draw a table and answer cumulative probability distribution problem below.
 * You draw two cards from standard 52 card deck. What is the probability that the sum is greater than 10 but less than 21? (Ace = 1)
 * A) 21 / 169
 * B) 45 / 169
 * C) 103 / 169
 * D) 154 / 169
 * E) None of the above


 * Value ||  Probability  ||
 * 2 ||  1/169  ||
 * 3 ||  2/169  ||
 * 4 ||  3/169  ||
 * 5 ||  4/169  ||
 * 6 ||  5/169  ||
 * 7 ||  6/169  ||
 * 8 ||  7/169  ||
 * 9 ||  8/169  ||
 * 10 ||  9/169  ||
 * 11 ||  10/169  ||
 * 12 ||  11/169  ||
 * 13 ||  12/169  ||
 * 14 ||  13/169  ||
 * 15 ||  12/169  ||
 * 16 ||  11/169  ||
 * 17 ||  10/169  ||
 * 18 ||  9/169  ||
 * 19 ||  8/169  ||
 * 20 ||  7/169  ||
 * 21 ||  6/169  ||
 * 22 ||  5/169  ||
 * 23 ||  4/169  ||
 * 24 ||  3/169  ||
 * 25 ||  2/169  ||
 * 26 ||  1/169  ||

p(10>x<21) = p(11) +p(12) + p(13) + p(14) + p(15) + p(16) + p(17) + p(18) + p(19) + p(20) = 103/136