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- 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 probabilitySuppose you have two boxes A and B. Box A contains 7 black marbles, 4 white marbles. Box B contains 7 white and 4 black marbles. A random experiment is performed in two sequential trials by first drawing a marble randomly from box A and putting into Box B. In the second trial after the first trial, a marble is drawn randomly from box B. If we reverse the scenario, then what is the probability of drawing a black marble from box A given that a white marble is drawn from box B.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
- EXERCISE - 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 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?
- If the probability of an event is 62%, what is the probability of its complement?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 rule2. Given a Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, Event A = {1, 3, 4, 7, 9}, and Event B = {3, 7, 9, 11, 12, 13} Find the probability P(A|B). State your answer as a value with one digit after the decimal point.
- Hypergeometric distribution Given user defined numbers k and n, if n cards are drawn from a deck, find the probability that k cards are black. Find the probability that at least k cards are black. INPUT 11 7 OUTPUT 0.1628063397551007 0.24927823677714275A fair coin is flipped 3 times. What is the probability that the flips follow the exact sequence below? Flip One: Heads Flip Two: Heads Flip Three: Tails ⅛ ⅜ ⅓ ⅔ ½Suppose that the length of a phone call in minutes is an exponential random variable with parameter λ=1/10. If someone arrives immediately ahead of you at a public telephone booth, find the probability that you will have to wait, (a) More than 10 minutes (b) Between 10 and 20 minutes