binomial distribution (w4) Flashcards
what does Probability (A | B) refer to
probability of obtaining A on the condition of B
for a coin toss, how would you write the probability of getting k heads in n tosses, when probability of getting heads for each toss is q (=0.5)
probability = Bi(k | n, q)
what is probability = Bi(k | n, q) considered to be?
a function that returns a value between 0 and 1 for given parameters k, n and q
what is probability of getting k number of heads out of n tosses
Bi(k | n, q) =
number of sequences with k−heads
/number of all possible sequences
what would a decision tree show for coin tosses
n coin toss can be visualised as a decision tree with n-layers after the top node
what is pascals triangle
tree of numbers where in a decision tree you write down numbers on each node as you go, add the 2 numbers on the nodes in the upper layer that are connected
how would you use pascals triangle
after filling in all the numbers, total number of possible sequences would be the sum of all numbers in the same layer, number on each node will be number of sequences for the corresponding k
eg if in layer 4 of pascals triangle each node had 1 , 4 , 6 , 4 , 1; what’s the probability of getting 3 heads and 1 tail
number of all possible sequences = 1 + 4 + 6 + 4 + 1 = 16
number of sequences with 3 heads = 4
Bi( 3 | 4, 0.5 ) = 4 / 16 = 0.25
how would you get probability distribution using pascals triangle, when is it called binomial distribution
write down probabilities in each node
when there are always 2 choices
what is cumulative probability
probability the value will fall within a certain range
how would you make: If you toss a coin 100 times, what is the probability of getting 40 heads? into a cumulative probability Q
If you toss a coin 100 times, what is the probability of getting less than 40 heads?
how would you write: what is the probability you get no more than 3 heads in 10 tosses
Bi ( 0 ≤ k ≤ 3 | 10, 0.5)
how would you calculate Bi ( 0 ≤ k ≤ 3 | 10, 0.5)
add up all the k’s in that range:
Pr ( 0 ≤ k ≤ 3 | 10, 0.5) = Pr (0 | 10, 0.5) + Pr (1 | 10, 0.5) + Pr (2 | 10, 0.5) + Pr (3 | 10, 0.5)
= 0.172 = cumulative probability
which probability is more rare: 0.377 or 0.0284
0.0284
how would you check the probability that data is deviated from the mean
take the cumulative probability at both ends, called the two-tailed probability
