Statistics Chapter 4: Discrete Variables

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What is the graph of a cumulative probability distribution called?

Ogive (correct)

Bar Chart

Histogram

Scatter Plot

What is the formula for the variance of a discrete random variable?

$\sigma^2 = \sum [x_i + E(X)]^2 P(X = x_i)$

$\sigma^2 = \sum [x_i - E(X)]^2 P(X = x_i)$ (correct)

$\sigma^2 = \sum [x_i - E(X)] P(X = x_i)^2$

$\sigma^2 = \sum [x_i - E(X)] P(X = x_i)$

What is the name of the probability distribution that is widely encountered in applied statistics?

Binomial Distribution (correct)

Normal Distribution

Uniform Distribution

Poisson Distribution

What is the formula for the expected value of a discrete random variable?

$E(X) = \sum x_i P(X = x_i)$ Signup and view all the answers

What is the standard deviation of a discrete random variable?

$\sigma = \sqrt{\sigma^2}$ Signup and view all the answers

What is the purpose of calculating the expected value of a discrete random variable?

To measure the center of the distribution Signup and view all the answers

What is the probability of getting exactly 3 successes in 10 trials, given a probability of success of 0.35 in each trial?

0.2522 Signup and view all the answers

What is the mean of a binomial distribution with n = 5 and p = 0.1?

0.5 Signup and view all the answers

Which of the following is a characteristic of the binomial distribution?

Discrete probability distribution Signup and view all the answers

What is the variance of a binomial distribution with n = 5 and p = 0.1?

0.6708 Signup and view all the answers

What is the Poisson distribution used for?

Modeling the probability of a number of independent events occurring in a fixed time Signup and view all the answers

What can be used to calculate the Binomial Distribution?

both statistical tables and Excel Signup and view all the answers

What is the primary characteristic of a discrete variable?

It produces outcomes that come from a counting process Signup and view all the answers

What is the purpose of a probability distribution in statistics?

To summarize the relationship between the values of a random variable and their probabilities Signup and view all the answers

Which of the following distributions is typically used to model the number of successes in a fixed number of independent trials?

Binomial Distribution Signup and view all the answers

What is the main difference between discrete and continuous variables?

Discrete variables produce outcomes that come from a counting process, while continuous variables produce outcomes that come from a measurement Signup and view all the answers

Which of the following distributions is typically used to model the number of events occurring in a fixed interval of time or space?

Poisson Distribution Signup and view all the answers

What is the purpose of learning about different types of probability distributions?

To calculate probabilities in real-world problems Signup and view all the answers