What is the sum of the probabilities in a probability distribution?

Expert Solution

The sum of the probabilities in a probability distribution is always 1.

A probability distribution is a collection of probabilities that defines the likelihood of observing all of the various outcomes of an event or experiment. Based on this definition, a probability distribution has two important properties that are always true:

Each probability in the distribution must be of a value between 0 and 1.

The sum of all the probabilities in the distribution must be equal to 1.

The sum of the probabilities in a probability distribution is always 1.

Nipun Maiti answered 2 years ago

What is the sum of the probabilities of all outcomes in a probability distribution? a. 0 b. 1/2 c. 1 d. It cannot be determined.

What is the sum of the probabilities of all outcomes in a probability distribution?a. 0b. 1/2c. 1d. It cannot be determined.

Use the probability distribution to find probabilities in parts (a) through (c). The probability distribution of...

Use the probability distribution to find probabilities in parts (a) through (c). The probability distribution of number of dogs per household in a small town Dogs 0 1 2 3 4 5 Households 0.6730.673 0.2010.201 0.0760.076 0.0250.025 0.0170.017 0.0080.008 (a) Find the probability of randomly selecting a household that has fewer than two dogs. 0.8740.874 (Round to three decimal places as needed.) (b) Find the probability of randomly selecting a household that has at least one dog. 0.3270.327 (Round...

preform a Monte Carlo simulation in R to generate the probability distribution of the sum of...

preform a Monte Carlo simulation in R to generate the probability distribution of the sum of two die (for example 1st die is 2 and second die is 3 the random variable is 2+3=5). The R-script should print out (display in R-studio) or have saved files for the following well labeled results: 1. Histrogram or barchart of probability distribution 2. Mean of probability distribution 3. Standard deviation of probability distribution

Give the expected value, variance, and probability distribution for the sum of a fair coin and...

Give the expected value, variance, and probability distribution for the sum of a fair coin and a random real number chosen uniformly in the range [ -1, 1]. Sketch the PMF.

Consider a Poisson probability distribution with lambda equals5.3 . Determine the following probabilities. a) exactly 5...

Consider a Poisson probability distribution with lambda equals5.3 . Determine the following probabilities. a) exactly 5 occurrences b) more than 6 occurrences c) 3 or fewer occurrences

DIRECTIONS: For items 1a-c The Cumulative Binomial Probability Distribution to determine the Cumulative Probabilities for the...

DIRECTIONS: For items 1a-c The Cumulative Binomial Probability Distribution to determine the Cumulative Probabilities for the Binomial Random Variable, X. 1a. According to the Gallup poll, P = 0.60 of U.S. women 18+ years of age stated that the minimum driving age should be 18. In a random sample of n = 15, U.S. women 18+ years of age, find the probability that: P(x < 5) believe that the minimum driving age should be 18 (1 pt): Between P (7...

Construct the discrete probability distribution for the random variable described. Express the probabilities as simplified fractions....

Construct the discrete probability distribution for the random variable described. Express the probabilities as simplified fractions. The number of heads in 5 tosses of a coin. Please answer in a table to understand better.

What is a probability distribution? What is a continuous probability distribution? Provide an example from business...

What is a probability distribution? What is a continuous probability distribution? Provide an example from business of the usefulness of a probability distribution and/or a continuous probability.

Consider the drawing of a probability tree for this data. What are the prior probabilities that...

Consider the drawing of a probability tree for this data. What are the prior probabilities that would be on the tree and what would they be for? WOMEN EYE COLOR CHILDREN 18 Brown No 22 Brown Yes 09 Blue No 21 Blue Yes 12 Green No 18 Green Yes MEN EYE COLOR CHILDREN 24 Brown No 16 ...

- What is a normal distribution and why is it useful for understanding probabilities and statistics?...

- What is a normal distribution and why is it useful for understanding probabilities and statistics? Provide an example of a normal distribution and explain why it can be categorized as a normal distribution. - What is the difference between a standard normal distribution and a normal distribution? - How do we standardize a normal distribution? - What is a z-score? How do we calculate the z-score for a normal variable? - How could the standard normal (z) distribution table...

Question