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Material Type: Exam; Class: Finite Probability & Applications; Subject: mathematics; University: Boston College; Term: Fall 2009;
Typology: Exams
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İlker S. Yüce December 7, 2009
A random variable Y is said to have a binomial distribution based on n trials with success probability if and only if P ( y ) = C ( n; k ) pkqn−k^ for k = 1 ; 2 ; : : : ; n and 0 ≤ p ≤ 1 and q = 1 − p. Complete table below for the binomial distribution n = 5 and p = : 5.
k P(Y=k) 0 1 2 3 4 5
Display the data from the table in a Histogram.
Let Y be a random variable distributed as shown in the accompanying table. Find the probabilities of the events P ( Y = 1), P ( Y > 1), P ( Y ≤ 3), P (2 ≤ Y ≤ 4), P ( Y ≤ 2 OR Y > 3), and P ( Y ≤ 3 AND Y > 2).
k P(Y=k)
In a gambling game a person who draws a jack or a queen is paid $15 and $5 for drawing a king or an ace from an ordinary deck of fifty-two playing cards. A person who draws any other card pays $4. if a person plays the game, what is the expected gain?
A heavy-equipment salesperson can contact either one or two customers per day with probability 1/3 and 2/3, respectively. Each contact will result in either no sale or a $50000 sale with the probabilities .9 and .1, respectively. Give the probability distribution for daily sales. Find the mean and standard deviation of the daily sales.
