Test Your Probability Knowledge

Random Variables and Probability Distributions

• Random Variable is a function that maps each sample point to a real number.
• Use uppercase letter to denote a random variable.
• Discrete Random Variables: finite number of possibilities or an unending sequence with as many elements as there are whole numbers.
• Continuous Random Variable: infinite number of possibilities equal to the number of points on a line segment.
• Probability Distributions: Cumulative distribution function (cdf), denoted by F(*) is defined by F(x)=P(X<=x).
• Discrete Probability Functions: a table or formula listing all possible values that a discrete random variable can take on along with the associated probabilities.
• Probability Mass Function: p(x) = P (X=x); mass points, values of X which p(x) > 0.
• Probability Density Functions: Continuous random variable X, which satisfies the following: f(x) >= 0 for all x, the total area under its curve = 1, and P(a <= X <= b) is the area bounded by the curve.
• Expected Value of X: Let X be a discrete random variable with probability mass function.
• Variance: Let X be the random variable with mean mu, then the variance of X is Var(X) = E[(X-mu)^2].
• Standard Deviation: the positive square root of variance; variance of X is a measure of dispersion.
• Binomial Experiment: possesses the following: the experiment consists of n identical trials, each trial results in one of 2 outcomes, a success or a failure, probability of a success on a single trial is equal to p and remains the same from the trial to trial, and trials are independent.
• Normal Distribution: a continuous random variable X is said to be normally distributed or follows normal distribution if its PDF is.

Test your knowledge on Random Variables and Probability Distributions with this quiz! Learn about the different types of random variables, probability distributions, and functions such as probability mass functions and probability density functions. Explore concepts such as expected value, variance, and standard deviation. See if you can identify binomial experiments and normal distributions. This quiz is perfect for anyone looking to improve their understanding of probability and statistics.