You are playing an exciting game of Battleship. Your opponent secretly positions ships

on a 10 by 10 grid and you try to guess where the ships are. Each of your guesses is a

hit if there is a ship there and a miss otherwise.

The game has just started and your opponent has 3 ships: a battleship (length 4), a

submarine (length 3), and a destroyer (length 2). (Usually there are 5 ships to start, but

to simplify the calculations we are considering 3 here.) You are playing a variation in

which you unleash a salvo, making 5 simultaneous guesses. Assume that your 5 guesses

are a simple random sample drawn from the 100 grid positions.

Find the mean and variance of the number of distinct ships you will hit in your salvo.

(Give exact answers in terms of binomial coefficient)

The number of people who visit the Leftorium store in a day is Pois(100). Suppose that

10% of customers are sinister (left-handed), and 90% are dexterous (right-handed). Half

of the sinister customers make purchases, but only a third of the dexterous customers

make purchases. The characteristics and behavior of people are independent, with probabilities as described in the previous two sentences. On a certain day, there are 42 people

who arrive at the store but leave without making a purchase. Given this information,

what is the conditional PMF of the number of customers on that day who make a

purchase?

62. A chicken lays n eggs. Each egg independently does or doesn't hatch, with probability p

of hatching. For each egg that hatches, the chick does or doesn't survive (independently

of the other eggs), with probability s of survival. Let N ? Bin(n, p) be the number of

eggs which hatch, X be the number of chicks which survive, and Y be the number of

chicks which hatch but don't survive (so X + Y = N). Find the marginal PMF of X,

and the joint PMF of X and Y . Are X and Y independent?

Solve the problem. We believe that 81% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 30 students from the population. If the true percentage is really 81%, find the probability of observing 29 or more students who consider statistics to be an exciting subject. Round to six decimal places. O0.985557 0.001797 0.014443 0.012646(X = 3) = 563 ( # 1 = 10 ( 1 ) = 3 Two video products distributors supply video ape boxes to a video production company. Company A sold 100 boxes of which 5 were efective. Company B sold 300 boxes of which 1 were defective. If a box was defective, find e probability that it came from Company B. Bayes' Theorem)Question 13 1 pointi Saved Artower Use a Venn Diagram and the given information to determine the number of elements in the Indicated region. At Southern State University IS50) there are 309 students baking Finite Mathematics or Mathers. 238 are taking Finke Mathematics, 104 are taking Statistics, and 23 are taking both Finite Mathematics and Statistics. How many are taking Finke Mathematics but riot Statistics Moving to another question will have the respons Question 13 0 132. Let X1,...,X ~i.i.d. Exp{). a. Find a consistent estimator for the second moment E(X2) (Hint: Weak Law of Large Numbers). Use the 1;;ng of X to prove that your estimator is consistent in the case a=1, =2. 13. Use the Central Limit Theorem to find the limiting distribution of an appropriately normalized version of your statistic. c. Find the pdf ofm