Basic Binomial Distribution
Flashcard
•
Mathematics
•
11th - 12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a Binomial Distribution?
Back
A Binomial Distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent states and is defined by two parameters: n (number of trials) and p (probability of success).
2.
FLASHCARD QUESTION
Front
What does P(X ≤ k) represent in a Binomial Distribution?
Back
P(X ≤ k) represents the probability that the random variable X is less than or equal to k, meaning it counts all outcomes from 0 to k.
3.
FLASHCARD QUESTION
Front
What does P(X ≥ k) represent in a Binomial Distribution?
Back
P(X ≥ k) represents the probability that the random variable X is greater than or equal to k, meaning it counts all outcomes from k to n.
4.
FLASHCARD QUESTION
Front
How do you calculate P(X = k) in a Binomial Distribution?
Back
P(X = k) is calculated using the formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where 'n choose k' is the binomial coefficient.
5.
FLASHCARD QUESTION
Front
What is the significance of the parameters n and p in a Binomial Distribution?
Back
n is the number of trials, and p is the probability of success on each trial. Together, they define the distribution.
6.
FLASHCARD QUESTION
Front
What is the difference between P(X < k) and P(X ≤ k)?
Back
P(X < k) represents the probability that X is less than k (not including k), while P(X ≤ k) includes k in the count.
7.
FLASHCARD QUESTION
Front
What does it mean to find the probability of 'at most k' in a Binomial Distribution?
Back
Finding the probability of 'at most k' means calculating P(X ≤ k), which includes all outcomes from 0 to k.
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