What are the two types of random variables

A regular deck of cards has 4 aces. You are asked to pick one card from the deck. If the card you picked is an ace you win $5! However if you pick any other card, you lose $2. If you play this game many times, on average how much would you expect to win?

The count of X successes in a binomial setting is a:

To find the mean of a binomial random variable

To find the mean/expected value for a geometric random variable

A  ____________ consists of repeated trials of the same chance process in which each trial results in a success or a failure, trials are independent, each trial has the same probability of success, and the goal is to count the number of trials until the first success occurs.

Suppose that a town is randomly selected from the state. Which of these pairs of random variables are most likely independent

If knowing whether any event involving X alone has occurred tells us nothing about the occurrence of any event involving Y alone, then X and Y are

What doe this formula calculate: x1p1+x2p2+x3p3+...=Σxipi

Is this a binomial setting? : Shuffle a deck of cards, turn over the first 7 cards, one at a time. Let Z= the number of Kings you observe

Is this a binomial setting?: Shuffle a deck of cards. Turn over the top card. Put the card back in the deck and shuffle again. Repeat until you get a queen. Let L=The number of trials until you get a queen

Is this a binomial setting?: Shuffle a deck of cards. Turn over the top card. Put the card back in the deck and shuffle again. Repeat until you get a queen. Let L=The number of trials until you get a queen

Is this a geometric setting?: Shake a bag of 30 marbles, with 10 red marbles, 10 blue marbles, and 10 green marbles. Reach into the bag and pull out a marble. Put the marble back in the bag and shake again. Repeat until you get a green marble. Let G=The number of trials until you get a green marble

You are to take a multiple choice exam consisting of 100 questions with five possible responses to each. Suppose you have not studied and decide to guess randomly on each question. Let X=# correct responses on the exam. What is your expected score on the exam?

Suppose 5% of cereal boxes contain a prize. You are determined to buy cereal boxes until you win a prize. What is the probability you will have to buy exactly 4 boxes?

Sally read that ⅙ eggs contains salmonella, so she only uses 10 eggs out of a dozen. If eggs do or don’t contain salmonella independently of each other, the number of contaminated eggs in a carton when Sally chooses 10 at random has the following distribution (based on chapter 6.3 review)

The _____ counts the number of ways k successes can be arranged among n trials

Find the geometric probability that Y=4 when the probability of success is .207

A potato chip company sells family sized bags labeled “10.5 ounces.” The probability that the total weight is less than 10.5 ounces for 1 randomly selected bag is approximately .136 ounces. If you randomly selected 10 bags of these chips, what’s the probability that exactly 2 of the bags will have a total weight less than 10.5 ounces?

The same potato chip company reports that their bags of family sized chips each follows an approx. Normal distribution with a mean of 10.72 ounces and a standard deviation of 0.2 ounces. If the company wants to ship these chips into boxes that contain 6 bags, what would be the mean and standard deviation of the total weight of a box containing 6 bags of chips? The empty boxes have a mean weight of 10 ounces and a standard deviation of 0.05 ounces

At a warehouse sale 100 customers are invited to choose one of 100 identical boxes. Five boxes contain $300 HD TVs, 25 boxes contain $150 camcorders, and the remaining boxes contain $75 digital cameras. What should a customer be willing to pay to participate in the sale?

An insurance company charges $800 annually for car insurance. The policy specifies that the company will pay $1000 for a minor accident and $5000 for a major accident. If the probability of a motorist having a minor accident during the year is .2, and of having a major accident, .05, how much can the insurance company expect to make on a policy?

During the years 1886 through 2000 there were an average of 8.7 tropical cyclones per year, of which an average of 5.1 became hurricanes. Assuming that the probability of any cyclone becoming a hurricane is independent of what happens to any other cyclone, if there are five cyclones in one year, what is the probability that at least three become hurricanes?

A coin is weighted so that the probability of heads is .75. The coin is tossed 10 times and the number of heads is noted. This procedure is repeated a total of 50 times, and the number of heads is recorded each time. What kind of distribution has simulated?