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Discrete Random Variables and Probability Distributions Quiz

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Discrete Random Variables and Probability Distributions Quiz

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Questions and Answers

In the experiment of tossing a coin 3 times, what is the sample space S?

{HH, HT, TH, TT}

{H, T}

{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} (correct)

{1, 2, 3}

What are the possible values of the discrete random variable X defined for the experiment of tossing a coin 3 times?

0, 1, 2, 3 (correct)

1, 2, 3, 4

1, 2, 3

0, 1, 2

How is the function X defined for the experiment of tossing a coin 3 times?

X = the product of the outcomes

X = the sum of the outcomes

X = the number of heads appeared (correct)

X = the average of the outcomes

What does it mean for a random variable to be discrete?

<p>The values of the random variable are countable and separate</p> Signup and view all the answers

Why is the function X considered random?

<p>Its values are related to the outcomes of a random experiment</p> Signup and view all the answers

Study Notes

Sample Space and Discrete Random Variable

The sample space S for the experiment of tossing a coin 3 times is the set of all possible outcomes, which is {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}.
The possible values of the discrete random variable X defined for the experiment of tossing a coin 3 times are the number of heads obtained in 3 tosses, which is {0, 1, 2, 3}.
The function X is defined as X(w) = number of heads in outcome w, where w is an element of the sample space S.
A random variable is discrete if it can only take on specific, distinct values.
The function X is considered random because its outcome is uncertain until the experiment is performed, and it is based on the outcomes of the 3 coin tosses.

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Description

Test your understanding of discrete random variables and probability distributions with this quiz. Explore an illustrative example of tossing a coin 3 times and defining the discrete random variable X as the number of heads that appear. Gain insight into the possible values of X and enhance your statistical knowledge.