Two teams A and B are playing against each other in a tournament. The first team to win 3 games is the champion. In each of the games, A has a probability of 0.25 to win, independent of the outcome of the previous games. Let random variable X represent the number of the games played.

(b) compute the PMF Px(x)

(d) During the tournament, team A was not able to win the tournament after the first 4 games. Compute the conditional PMF PX|X>4 (x)

A survey reported that 37% of people plan to spend more on eating out after they retire. If

eight people are randomly​ selected, determine the values below.

You are manager of a ticket agency that sells concert tickets. You assume that people will call 4 times in an attempt to buy tickets and then give up. Each telephone ticket agent is available to receive a call with probability 0.25. If all agents are busy when someone calls, the caller hears a busy signal.

Find n, the minimum number of agents that you have to hire to meet your goal of serving 95% of the customers calling to buy tickets.

In comparing probability distributions, which of the following statements is TRUE?

Select one:

2. The exponential and Poisson distributions are interchangeable because they have the exact same
random variable.

3. The geometric and negative binomial distributions both have a random number of trials.

4. The uniform and normal distributions have the same distribution shapes.

5. The Poisson distribution is the limiting form of the negative binomial distribution.

a. A stock has an annual return of 14 percent and a standard deviation of 62 percent. What is the smallest expected loss over the next year with a probability of 1 percent? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Round the z-score value to 3 decimal places when calculating your answer. Enter your answer as a percent rounded to 2 decimal places.)

b. Does this number make sense?

• Yes

• No

Let suppose you roll a die, and it falls into a hidden place, for example under furniture.
Then although the experiment has already been made (the die already has a number to show), that value can not be known, so the experiment was not fully realized.
Then till you see the die's top side, the probability remain p = 1/6.
I see no difference between this and the wave function collapse, at least as an analogy.
Can someone explain a deeper difference?

There is a chess team with four players {A, B, C, D} training for a competition. The coach wants all players to play each other. Ignore which player is chosen to take the first move.

1. Do we use a counting rule for combinations or for permutations to calculate the total number of possible games if all players must play each other once? (Only one is correct.)

2. Calculate by hand (you can use a calculator but show some work), how many games will there be if all players must play each other once?

3. If we have players {A, B, C, D} and two players will be selected at random for a challenge. What is the probability that players A and B are chosen to play? This follows from your answer from part (b). (By the way, this is the same probability of any two players being chosen.)

Barron's reported that the average number of weeks an individual is unemployed is 15 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 15 weeks and that the population standard deviation is 6 weeks. Suppose you would like to select a sample of 65 unemployed individuals for a follow-up study. Use z-table.

a. Show the sampling distribution of X bar, the sample mean average for a sample of  unemployed individuals.

b. What is the probability that a simple random sample of 65 unemployed individuals will provide a sample mean within 1 week of the population mean?

(to 4 decimals)

c. What is the probability that a simple random sample of 65 unemployed individuals will provide a sample mean within 1/2 week of the population mean?

(to 4 decimals)

According to a Pew Research study from March, 2016, 28% of all adult Americans have read an e-book in the last 12 months. Assume that 28% of all adult Americans have read an e-book in the last 12 months. A random sample of 75 adult Americans is selected. Let the random variable X represent the number of adult Americans, out of the 75, who have read an e-book in the last 12 months.

a. Use the Binomial Formula to find the probability that exactly 25 of the 75 adult Americans will have read an e-book in the last 12 months.

b. Compute the mean of this distribution and state what it represents.

c. Use the normal approximation for X to find the probability that more than 20 of the 75 adult Americans will have read an e-book in the last 12 months.