Probability and Statistical Inference 2024 Question and Answers Final Exam

Probability and Statistical Inference 2024 Question and Answers Final Exam What is the probability of picking 3 queens in a row from a deck of 52 cards. Order is noted and cards are not replaced Counting problem. (432)/(525150) The probability that a WWU student pulls an all-nighter on a given day is 30%. Let X = the number of students out of 12 who pull an all-nighter tonight. Assuming that students "independently" choose to pull all-nighters: What is P(X=4): (12CX)(.3^x)(1-.3)^(12-x) = .231 The probability that a WWU student pulls an all-nighter on a given day is 30%. Let X = the number of students out of 12 who pull an all-nighter tonight. Assuming that students "independently" choose to pull all-nighters: What is the expected value of the associated distribution: NP = 3.6 IF the number of spelling errors per page is know to be Poisson(2), then: What is the probability that there are no mistakes on one page: e^-2 * 2^0 / 0! = .135 IF the number of spelling errors per page is know to be Poisson(2), then: What is the probability that there are at least 2 mistakes on 3 pages SO inf E x=2 (e^-6 * 6^x) / X! What is the mean of the following distribution: f(x) = (5Cx).2^x * .8^(5-x) x=0,1,2,3,4,5 5 * .2 = 1 Binomial NP = mean What is the mean of the following distribution: f(x) = e^-1/x! x=0,1,2,3..... e^-1 * 1^x/ X! x=1 Poisson You are told that the following function is a pmf: f(x) = cx where outcome space is x=1,2. Find c (1)C + 2C = 1 (all outcome spaces most add up to 1) 3C= 1 c = 1/3 You are told that the following function is a pmf: f(x) = cx where outcome space is x=1,2. What is the expected value of the pmf: 1/3 1 + 1/32^2 = 5/3 Give the probability of randomly selecting the point 1.8 from the interval [1,2] if each point is equally likely: 0 Give the definition of mutually exclusive events IF A union B = Null set Give an example of 2 complementary events Raining / not raining Give an example of a random experiment with a discrete outcome space rolling a 6 sided die 4 times and counting how many times 1 was rolled How man possible letter formations can be formed from the following using all letters in each word: acid 4! = 24 How man possible letter formations can be formed from the following using all letters in each word: bookkeeper Boy-girl problem. (10C1)(9C2)(7C2)(5C3)(2C1)(1C1) I own 4 pairs of pants, 3 shirts and 4 pairs of shoes: How many different outfits can i create?(Assume that you must wear one pair of shoes, one shirt, and one pair of pants) (5C1)(4C1)(4C1) = 80 I own 4 pairs of pants, 3 shirts and 4 pairs of shoes: If i go t a "Crazy Outfit Party" and am supposed to wear exactly 2 pairs of pants at once, exactly 3 pairs at once and at least 2 pairs of shoes, then how many different outfits can i create? (5c2)(4c3)(4c2) + (5c2)(4c3)(4c3) + (5c2)(4c3)(4c1) = 440 You are told that the P(A) is twice P(B) and that A and B are exhaustive events. If P(A and B) = .2 then are A and B independent? P(A) + P(B) - P(A intersect B) = 1 not independent Consider the Math 341 student who sits at home Friday nights, drawing 5 cards from a deck, pondering the following probailities: What is the probability of drawing an ace, then another ace, then a 6, then another 6 then another ace in that order (43432)/() Consider the Math 341 student who sits at home Friday nights, drawing 5 cards from a deck, pondering the following probailities: what is the probability that a second card drawn is red given that the first card drawn is red P(A interesect B) / P(B) = 26/52 * 25/51 / 26/52 Consider the Math 341 student who sits at home Friday nights, drawing 5 cards from a deck, pondering the following probailities: What is the probability that 2 of the cards are spades, 2 of the cards are hearts and one of the cards is diamonds in any order ((31c1)(12c1)(13c1)(12c1)(13c1)/(52c5)) *5! = .005 The number of UFO sightings over a bakery that serves world famous fish flavored pastries, is known to follow a Poisson distribution. IF an average of 3 are sighted per half-hour, then what is the probability that you sight 2 in 1 hour e^-6 * 6^2/2! The number of UFO sightings over a bakery that serves world famous fish flavored pastries, is known to follow a Poisson distribution. IF an average of 3 are sighted per half-hour, then What is the probability that you wait exactly 30 minutes for the next UFO sighting 0 The number of UFO sightings over a bakery that serves world famous fish flavored pastries, is known to follow a Poisson distribution. IF an average of 3 are sighted per half-hour, then What is the probability that you wait more than 2 hours for the next UFO sighting P(w>2) lambda = 12, e^-12 * 12^0 / 0! From a group of 10 people, 4 males and 6 females: How many ways can you line the people up 10! = 3,628,800 From a group of 10 people, 4 males and 6 females: How many ways can you the line the people up if you just differentiate by the gender of the individual (10N4)(6N6) = 210 From a group of 10 people, 4 males and 6 females: What is the probability that a committee of size 5 has exactly 3 males Combinations: 5 people, 3 males (4N3)(6N2)/(10N5)