Random Variables Flashcard

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.

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.

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.

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.

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.

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.

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.

Front

Explain the concept of 'at least' in probability.

Back

'At least' refers to the probability of achieving a certain number of successes or more, often calculated by summing the probabilities of all outcomes greater than or equal to that number.

Front

What is the difference between discrete and continuous random variables?

Back

Discrete random variables can take on a countable number of values, while continuous random variables can take on an infinite number of values within a given range.

Front

What is a histogram in the context of probability distributions?

Back

A histogram is a graphical representation of the distribution of numerical data, showing the frequency of data points within specified ranges.