# Probability - Random Variables

• tjackson
Can you please clarify what it stands for? In summary, the conversation discussed completing a test with 10 true-false questions and a student answering them by flipping a coin. The number of correctly answered questions can be represented by X, and the distribution of X is binomial. The probability of answering at most 5 of the questions correctly is calculated using the binomial cumulative distribution function (binomcdf). The conversation also confirmed that the given values for p, k, and n are correct.
tjackson

## Homework Statement

1. A test consists of 10 true-false questions.
(a) In how many ways can it be completed? (HINT: The task of completing the test consists
of 10 stages. Use the Product Rule.)

(b) A student answers the questions by
flipping a coin. Let X denote the number of correctly
(i) The distribution of X is:

binomial
hypergeometric
negative binomial
Poisson

(ii) Find the probability he/she will answer correctly at most 5 of the questions.

## Homework Equations

/ Attempt at a solution

a) i believe this is just 210?

b.) i.) is this binomial??

ii.) $\stackrel{n}{k}$ * pk * (1-p)(n-k)

p = 1/2
k = 5
n = 10

$\stackrel{n}{k}$
is n choose k

a)correct
b)binomial
binomcdf(10,.5,5)

It's been awhile since I took statistics. There is a chance I'm wrong.

FileDeleted said:
a)correct
b)binomial
binomcdf(10,.5,5)

It's been awhile since I took statistics. There is a chance I'm wrong.

RGV

So these statements are correct?

p = 1/2
k = 5
n = 10

I apologize, I am not familiar with the 'binomcdf(10,.5,5)' format

## 1. What is a random variable?

A random variable is a mathematical concept that represents a numerical outcome of a random event. It can take on different values based on the outcome of the event and is often denoted by the letter X.

## 2. What is the difference between discrete and continuous random variables?

Discrete random variables can only take on a finite or countably infinite number of values, while continuous random variables can take on any value within a given range. For example, the number of heads obtained when flipping a coin is a discrete random variable, while the height of a person is a continuous random variable.

## 3. How is probability related to random variables?

Probability is the likelihood or chance of a particular outcome occurring. Random variables allow us to assign probabilities to different outcomes, which helps us understand and analyze the behavior of random events.

## 4. What is the expected value of a random variable?

The expected value of a random variable is the average value we would expect to obtain if we were to repeat the experiment many times. It is calculated by multiplying each possible outcome by its corresponding probability and summing them all together.

## 5. Can random variables be used to model real-life situations?

Yes, random variables are commonly used in statistical models to represent real-life situations. For example, they can be used to model the probability of a certain outcome in a clinical trial or the likelihood of a particular event occurring in an economic forecast.

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