Bayes rule is given as: P(AIB) = P(BIA) P(A)/P(B) Consider a party where male and not male guest arrive with their choice of dress color. Some pink and others are not. Following is the data about observations of guests and their color choices: Pink notPink Man 5 35 notMan 20 40 Using this data find the probability: P(Pink Man). Show your calculations and the result
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- A certain cat shelter has devised a novel way of making prospective adopters choose their new pet. To remove pet owners’ biases regarding breed, age, or looks, they are led blindfolded into a room containing all the cats up for adoption and must bring home whichever they pick up. Suppose you are trying to adopt two cats, and the shelter contains a total of N cats in one of only two colors: black or orange. is it still possible to pick up two black cats with probability ½, given that there is an even number of orange cats in the room? If so, how many cats should be in the room? How many black, how many orange?You are given the following data: vocabulary V = {w1, w2, w3} and the bigram probability distribution p on V × V given by: p(w1, w1) = 1/4 p(w3, w3) = 1/8 p(w2, w2) = 0, p(w2, w1) = 1/4, p(w1, w3) = 1/4, p(w1, *) = 1/2 (that is w1 as the first of a pair), p(*, w2) = 1 /8 . Calculate p(w1, w2) and p(w2 | w3) using Markov's ruleEXERCISE - You go to a market to pick out some gourds to decorate your house for Halloween. The market has a special October deal where you get 3 randomly chosen gourdss for $10. Each gourd can either be an orange pumpkin, a green pumpkin or a squash. The probabilities for picking each one of them are: P(orange pumpkin) = 0.6, P(green pumpkin) = 0.3, and P(squash) = 0.1. A: What is the probability that the first gourd is an orange pumpkin, the second is a green pumpkin, and the third is a squash? B: What is the probability that you get all 3 as orange pumpkins? C: What is the probability that you get no squashes? D: What is the probability that you get at least one orange pumpkin? (ANSWERE USING PYTHON)
- Three coins are tossed at the same time, each equally likely to come up heads or tails. What is the probability of getting 1 head and 2 tails?A typical roulette wheel used in a casino has 38 slots that are numbered 1,2,3,....,36,0,00, respectively. Half of the remaining slots are red and half are black. Also, half of the integers between 1 and 36 inclusive are odd, half are even, and 0 and 00 are defined to be neither odd nor even. A ball is rolled around the wheel and ends up in one of the slots; we assume each slot has equal probability of 1/38, and we are interested in the number of the slot into which the ball falls. (a)Define the Sample space S. (b)Let A = {0,00}. Give the value of P(A). (c) Let B = {14,15,17 18}. Give the value of P(B). (d) Let D = {x:x is odd}. Give the value of P(D).Let X and Y be two binary, discrete random variables with the following joint probability mass functions. (a) Compute P(X = 0]Y = 1). (b) Show that X and Y are not statistically independent. P(X = 0, y = 1) = P(X = 1, Y = 0) = 3/8 P(X = 0, y = 0) = P(X = 1, Y = 1) = 1/8
- Give an example of a random variable X : {b, c, d, e} → N (Natural Number) with expectation 2, where each of {b, c, d, e} has equal probabilityA set of 30 event tickets are placed in a bag. There are 6 baseball tickets, 4 hockey tickets, 4 basketball tickets, 2 football tickets, 3 symphony tickets, 2 opera tickets, 4 ballet tickets, and 5 theater tickets. One ticket is selected without looking. Find each probability. (Show your work) a)P(not a basketball tickets ) b)P(opera or ballet) c) P(not a symphony or not sport ) d)P( not Baseball and not Sport )Please don't copy If μ=0.9, use the Hoeffding Iequality to bound the probability that a sample of 10marbles will have ν≤0.1 and compare the answer to the pervious problem
- A random variable X with two-sided exponential distribution given by has moment generating function given by M X (t)= e^ t +e^ -t -2 t^ 2 . f x (x)= x+1,&-1\\ 1-x,&0<= x<=1 - 1 <= x <= 0 (a) Using M_{X}(t) or otherwise, find the mean and variance of X. (b) Use Chebychev inequality to estimate the tail probability, P(X > delta) , for delta > 0 and compare your result with the exact tail probability.So I have the following roshambo strategy function to return a random play, and tests for when one of the length of plays is less than 3 and otherwise. I have tried running it many times on a single scenario to estimate the probability for each return but the results are somehow confusing. Question: Write a series for the roshambo function below to test that it works as expected. (this could be testthat::expect_equal or testthat::expect_true or testthat::expect_error tests). Thank you. roshambo <- function(plays){ # return random play if (length(plays) < 3){ return(sample(c("R", "P", "S"), 1)) } # else find most common most_common <- names(which.max(table(plays))) if (most_common == "S"){ return("R") } else if (most_common == "R"){ return("P") } else { return("S") }}Find the probability that the same fair dice will appear two rounds in a row in Backgammon. For example, {3,3} coming again after throwing {3,3}; or the probability of getting {2.5} in the second hand after the first hand {2.5}.