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QUESTION 1 Let X be a random variable representing the number of total children in a typical American family. The distribution of X is as follows: The Number P(X=X) of Children (X) 0 15 1 .25 2 .35 3 .20 4 .04 5 .01 Please Note: The probability of 6 or more children is very small and was rounded off to 0. Is the data in the above table a legitimate probability distribution? A) No, 0+1+2+3+4+5=15 B) No, 0 cannot be one of the values of X. C) Yes, since X is a random variable. D) Yes, since the probabilities are between zero and one, inclusive, and they sum to one. . QUESTION 2 Assume the table in the previous problem is a legitimate probability distribution (it may or may not be). What is the expected value of X? A) 1.76 B) .2 C) 1 D) Cannot tell from this information QUESTION 3 Assume the probability of having a daughter born is .51. Let X= the number of daughters a family has. If a family has 5 children (n=5) what is the probability of having one daughter or less (P(X51)? (Hint: Use the binomial distribution) A) . 175 B) .49 C) .51 D) .825 QUESTION 4 The probability that a field hockey player scores a goal in any game is .2 (either the player scores or doesn't score, we don't care how many goals). Let X= the number of games the player scores a goal. Assume that the season is 25 games. If we assume that X is a random variable and follows a binomial distribution, in how many games do we expect this player to score? A) 25 B) .2 C) 2 D) 5 QUESTION 5 Assume you flip a coin 100 times and get 60 heads. You immediately get suspicious about this coin. After all, if X is a random variable, X=the number of heads, and P(X)=.5, you should have expected around 50 heads if this was a fair coin. Being a Statistics student and assuming X follows a binomial distribution, you calculate the mean and standard deviation of X. Using the empirical rule, what can you conclude about this coin? A) The coin is biased because we didn't get 50 heads. B) The coin is biased because 95% of the time we expect 50 heads. C) The coin is fair because 95% of the time we expect 40 to 60 heads. D) The coin is fair because 99% of the time we expect 40 to 60 heads