Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and... Problem 1.2P: How many outcome sequences are possible ten a die is rolled four times, where we say, for instance,... Problem 1.3P: Twenty workers are to be assigned to 20 different jobs, one to each job. How many different... Problem 1.4P: John, Jim, Jay, and Jack have formed a band consisting of 4 instruments if each of the boys can play... Problem 1.5P: For years, telephone area codes in the United States and Canada consisted of a sequence of three... Problem 1.6P: A well-known nursery rhyme starts as follows: As I was going to St. Ives I met a man with 7 wives.... Problem 1.7P: a. In how many ways can 3 boys and 3 girls sit in a row? b. In how many ways can 3 boys and 3 girls... Problem 1.8P: When all letters are used, how many different letter arrangements can be made from the letters a.... 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![4 Iron ore is dug up to be crushed and filtered through a sieve prior to further processing. The
sieve filters out any iron ore larger than 1cm in diameter. Let X be a random variable describing
the diameter (in cm) of a piece that has made it through the sieve. Suppose that X has the
beta distribution with parameters a = 4 and ß = 3.
(a) Determine the cdf of X.
(b) Calculate the mean and standard deviation of the diameter of iron ore pieces.
(c) The dollar value V of an iron ore piece is proportional to its volume, specifically V = $ 5X³.
Find E[V], the average dollar value of a piece that makes it through the sieve.](https://content.bartleby.com/qna-images/question/eaf0af2a-3abd-4b05-8a4d-6ad3e8b11589/dc8320b5-63f0-4b97-a2c1-a17fc2307fdf/sjaz2ip_processed.png)
