Take 3 dice and throw these dice 30 times. Let X be the sum of the number of dots on upper faces of the dice.

Obtain probability distribution of X. Also find mean and variance.

6. Team A and Team B are competing in the following game: There are 25 flags planted on the beach. On its turn a team may take 1, 2, 3, or 4 flags. The team that takes the last flag wins. Team A chooses first. You are the captain of Team B. Using backward induction, devise and explain a strategy that guarantees your team will win.

1. Team A and Team B are competing in the following game: There are 25 flags planted on the beach. On its turn a team may take 1, 2, 3, or 4 flags. The team that takes the last flag wins. Team A chooses first. You are the captain of Team B. Using backward induction, devise and explain a strategy that guarantees your team will win.

India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the birth rate, especially in rural India, is still too high to be sustainable. A demographer assumes the following probability distribution for the household size in India.

a. What is the probability that there are less than 5 members in a household in India? (Round your answer to 2 decimal places.)

b. What is the probability that there are 5 or more members in a household in India? (Round your answer to 2 decimal places.)

c. What is the probability that the number of members in a household in India is strictly between 2 and 5? (Round your answer to 2 decimal places.)

i) Plot a cumulative probability distribution similar to the one in the coin

toss experiment, but for the probability of the number of sixes rolled in 10

rolls of a die (a die has 6 sides!).

ii) If we observe four sixes in 10 rolls, is this die likely to be loaded? If we observe a six four times out ten what is a 95% confidence interval on the underlying probability of rolling a six?

iii) Say instead we had rolled 40 sixes out of 100. Is the die likely to be loaded? What is a 95% confidence interval on the probability of rolling a six?

iv) Say instead we had rolled 400 sixes out of 1000. Is the die likely to be loaded? What is a 95% confidence interval on the probability of rolling a six? Hint: use binom.test() for parts ii-iv.

Work needs to be done in Rstudio

The quality control manager of​ Marilyn's Cookies is inspecting a batch of​ chocolate-chip cookies that has just been baked. If the production process is in​ control, the mean number of chip parts per cookie is 6.3. Complete parts​ (a) through​ (d). (Round to four decimal places as​ needed.)

a. What is the probability that in any particular cookie being inspected fewer than five chip parts will be​ found?  

The probability that any particular cookie has fewer than five chip parts is ? ​(Round to four decimal places as​ needed.)

b. What is the probability that in any particular cookie being inspected exactly five chip parts will be​ found?

c. What is the probability that in any particular cookie being inspected five or more chip parts will be​ found?

d. What is the probability that in any particular cookie being inspected either four or five chip parts will be​ found?

You are a surgical oncologist who specializes who specializes in removing liver tumors. You classify a surgery as a success if all tumor tissue is removed, and a failure if it is not. Each surgery has a probability of success p. You only perform one surgery per patient, and the surgeries are independent events, so you can consider each surgery as a Bernoulli trial.

1.  What is the probability of having at least 7 successes is you perform 10 surgeries with p = 0.75. Note that this is different than the question of having 7 successes if you perform 10 surgeries with p = 0.75. This question is asking for the probability that k ≥ 7, not just the probability that k = 7.

2. Suppose that you perform 10 different surgeries and p = 0.75. Make a graph with "number of successful surgeries" plotted on the horizontal axis and "probability" plotted on the vertical axis.

I need a step by step for entering in excel.

For this assignment, your group will utilize the preliminary data collected in the Topic 2 assignment. Considering the specific requirements of your scenario, complete the following steps using Excel. The accuracy of formulas and calculations will be assessed.

1. Select the appropriate discrete probability distribution. If using a binomial distribution, use the constant probability from the collected data and assume a fixed number of events of 20. If using a Poisson distribution, use the applicable mean from the collected data.
2. Identify the following: the probability of 0 events occurring, the probability of <5 events occurring, and the probability of ≥10 events occurring.
3. Using the mean and standard deviation for the continuous data, identify the applicable values of X for the following: Identify the value of X of 20% of the data, identify the value of X for the top 10% of the data, and 95% of the data lies between two values of X.