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Questions and Answers
What is a random variable?
What is a random variable?
- A function that maps each sample point to a real number. (correct)
- A function that maps each sample point to another sample point.
- A function that maps each real number to another real number.
- A function that maps each real number to a sample point.
Which letter is used to denote a random variable?
Which letter is used to denote a random variable?
- Uppercase letter (correct)
- a
- b
- c
What is a discrete random variable?
What is a discrete random variable?
- A variable with an infinite number of possibilities.
- A variable with a continuous range of possibilities.
- A variable with a probability of 0.
- A variable with a finite number of possibilities. (correct)
What is a probability distribution?
What is a probability distribution?
What is a probability density function?
What is a probability density function?
What is the expected value of X?
What is the expected value of X?
What is a binomial experiment?
What is a binomial experiment?
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Study Notes
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.
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