Random Variables Flashcard

Flashcard
•
Mathematics
•
12th Grade
•
Hard
+4
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a random variable?
Back
A random variable is a numerical outcome of a random phenomenon, which can take on different values based on the outcome of a random event.
2.
FLASHCARD QUESTION
Front
Define probability distribution.
Back
A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take.
Tags
CCSS.HSS.MD.A.3
CCSS.HSS.MD.A.4
3.
FLASHCARD QUESTION
Front
What is the mean of a probability distribution?
Back
The mean of a probability distribution, also known as the expected value, is the average of all possible values, weighted by their probabilities.
Tags
CCSS.HSS.MD.A.2
4.
FLASHCARD QUESTION
Front
How do you calculate the standard deviation of a probability distribution?
Back
The standard deviation is calculated as the square root of the variance, which measures the spread of the probability distribution.
5.
FLASHCARD QUESTION
Front
What does it mean for a distribution to be valid?
Back
A valid probability distribution must satisfy two conditions: all probabilities must be between 0 and 1, and the sum of all probabilities must equal 1.
Tags
CCSS.HSS.MD.A.3
CCSS.HSS.MD.A.4
6.
FLASHCARD QUESTION
Front
What is the formula for calculating the probability of getting exactly k successes in n trials?
Back
The formula is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where p is the probability of success.
Tags
CCSS.HSS.MD.A.4
CCSS.HSS.MD.A.3
7.
FLASHCARD QUESTION
Front
What is the binomial distribution?
Back
The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.
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