Binomial and Geometric Distribution

Flashcard
•
Mathematics
•
12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the expected value in a probability distribution?
Back
The expected value is the long-term average or mean of a random variable, calculated as the sum of all possible values, each multiplied by its probability.
2.
FLASHCARD QUESTION
Front
What are the assumptions of the Binomial distribution?
Back
1. Fixed number of trials 2. Each trial is independent 3. Each trial has only two outcomes (success or failure) 4. The probability of success is constant across trials.
3.
FLASHCARD QUESTION
Front
What is a discrete random variable?
Back
A discrete random variable is one that can take on a countable number of distinct values, such as the number of successes in a series of trials.
4.
FLASHCARD QUESTION
Front
What is a geometric distribution?
Back
A geometric distribution models the number of trials needed to achieve the first success in a series of independent Bernoulli trials.
5.
FLASHCARD QUESTION
Front
How do you calculate the expected value of a Binomial distribution?
Back
E(X) = n * p, where n is the number of trials and p is the probability of success.
6.
FLASHCARD QUESTION
Front
What is the difference between discrete and continuous random variables?
Back
Discrete random variables take on countable values, while continuous random variables can take on any value within a given range.
7.
FLASHCARD QUESTION
Front
What is the formula for the probability mass function of a Binomial distribution?
Back
P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success.
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