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Probability and Statistics Quiz

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Questions and Answers

What is a possible value of X for the difference between the number of heads and tails when a coin is tossed 6 times?

8
7
4 (correct)
3 (correct)

In the scenario of drawing two balls from an urn containing 5 red and 2 black balls, what are the possible values of X, the number of black balls drawn?

3
4
2 (correct)
5

Which of the following sets is not a probability mass function (PMF)?

P(X) where P(0) = 0.1, P(1) = 0.5, P(2) = 0.2, P(3) = -0.1, P(4) = 0.2 (correct)
P(X) where P(0) = 0.4, P(1) = 0.4, P(2) = 0.2
P(Z) where P(3) = 0.3, P(2) = 0.2, P(1) = 0.4, P(0) = 0, P(-1) = 0.05
P(X) where P(0) = 0.1, P(1) = 0.6, P(2) = 0.3

From the following, which option denotes a valid probability mass function?

<p>P(X) where P(0) = 0.4, P(1) = 0.4, P(2) = 0.2 (B), P(X) where P(0) = 0.1, P(1) = 0.6, P(2) = 0.3 (D)</p> Signup and view all the answers

Which condition must a function meet to be classified as a probability mass function?

<p>The sum of probabilities must equal 1. (C)</p> Signup and view all the answers

Flashcards

Random Variable

A variable whose value is a numerical outcome of a random phenomenon. It can take on different values with different probabilities.

Possible Values (X)

The set of all possible numerical outcomes that a random variable can take on.

Probability Mass Function (PMF)

A function that associates each possible value of a discrete random variable with its probability of occurrence.

Characteristics of a PMF

A valid PMF must have the following properties: 1. All probabilities are non-negative. 2. The sum of all probabilities equals 1.

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Valid PMF?

To determine if a function is a valid PMF, check if all probabilities are non-negative and if their sum equals 1.