Question: 5. The probability that a letter will be delivered within three working days is 0.9. You send out 10 letters on Tuesday to invite friends

5. The probability that a letter will be delivered within three working days is 0.9. You send out 10 letters on Tuesday to invite friends for dinner. Only those who receive the invitation by Friday (i.e., within 3 working days) will come. Let X denote the number of friends who come to dinner.

(a) The random variable X is (choose one)

(i) binomial (ii) hypergeometric (iii) negative binomial

(iv) Poisson.

(b) Give the expected value and variance of X.

(c) Determine the probability that at least 7 friends will come.

(d) A catering service charges a base fee of $100 plus

$10 for each guest coming to the party. What is the expected value and variance of the catering cost?

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