Give the PMF of X and the probabilities of X in [0,2) or (2,+∞) or (-∞,2].
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There are four defective products in ten products, of which two are randomly selected. Take X as the number of defective products contained in the two selected products. Give the PMF of X and the probabilities of X in [0,2) or (2,+∞) or (-∞,2].
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- Let A, B, and C be independent random variables, uniformly distributed over [0,3], [0,2], and [0,4] respectively. What is the probability that both roots of the equation Ax2Bx+C = 0 are real?A group of researchers wishes to see if the total number of diseases that occurred in six countries are the same. The data are shown in the table. At α = 0.05 is there enough evidence to reject the claim that the number of diseases in the six countries are the same? Philippines - 8,6,7,10,16 India -6,13,16,10,7 Thailand. -5,8,16,22,12 Singapore. -14,12,8,9,15 Korea. -5,4,32,21,17 Japan. -6,18,15,24,16A report just came out that stated that 21.1% of all Americans say that vanilla is their favorite ice cream, 20.9% say that chocolate is their favorite, 9.1% favor butter pecan, 9.5% favor strawberry, and the rest have other favorites. An ice cream shop owner thinks that her customers are not like the rest of America. The table below shows the results of 980 of her patrons' ice cream selections. What can be concluded at the αα = 0.10 significance level? Complete the table by filling in the expected frequencies. Round your answers to the nearest whole number.Frequencies of Favorite Ice Cream Outcome Frequency Expected Frequency Vanilla 217 Chocolate 209 Butter Pecan 107 Strawberry 80 Other 367 What is the correct statistical test to use?Select an answer Homogeneity Goodness-of-Fit Paired t-test Independence What are the null and alternative hypotheses?H0:H0: Favorite ice cream and where the ice cream is purchased are dependent. The distribution…
- An electronics store has received a shipment of 20 table radios that have connections for an iPod or iPhone. Ten of these have two slots (so they can accommodate both devices), and the other ten have a single slot. Suppose that six of the 20 radios are randomly selected to be stored under a shelf where the radios are displayed, and the remaining ones are placed in a storeroom. Let X = the number among the radios stored under the display shelf that have two slots. (a) What kind of distribution does X have (name and values of all parameters)? O hypergeometric with N = 10, M = 6, and n = 10 O binomial with n = 20, x = 10, and p = 6/20 hypergeometric with N = 20, M = 10, and n = 6 O binomial with n = 10, x = 6, and p = 6/10 (b) Compute P(X= 2), P(X ≤ 2), and P(X ≥ 2). (Round your answers to four decimal places.) P(X = 2) = P(X ≤ 2) = P(X ≥ 2) = (c) Calculate the mean value and standard deviation of X. (Round your standard deviation to two decimal places.) mean value standard deviation…Define β1 stands for?Suppose that A and B are independent events such that =PA0.30 and =PB0.40 . Find P∩AB and P∪AB . (If necessary, consult a list of formulas.) (a) =P∩AB (b) =P∪AB
- Suppose 2 docoss A and B test all into patients coming for syphilis. Let At ={ doctor Á makes a a clinic pesitive diagnosis} and Bt = { docbr B makes a postive diagnosis} %3D Suppose doctor A A diagnoses 10%% of all patients as postive, positive and both as docfor B diaanoser 17% of all patientsLet X and Y be two random variables such that Cov(X.Y) = -3 . Then %3D O None of these O cov(-3X+5,-3Y+5)=-18 cov(3X+5,-2Y+5)=18 O cov(5X+3,-2Y-2)=-204 Suppose that Alejandro is planting a garden of tulips. Let X be the Bernoulli random variable that returns 1 if the tulip is red, and 0 otherwise. Suppose Y is another Bernoulli random variable, independent of X, that returns 1 if the tulip survives longer than 30 days, and 0 otherwise. Both X and Y have parameters 1/2. Let Z be the random variable that returns the remainder of the division of X +Y by 2. For example, if X = 1 and Y = 0, Z = remainder() = 1 (a) Prove that Z is also a Bernoulli random variable, also with parameter 1/2. (b) Prove that X, Y, Z are pairwise independent but not mutually independent. (c) By computing Var[X+Y+Z] according to the alternative formula for variance and using the variance of Bernoulli r.v.'s, verify that Var[X+Y+Z] = Var[X]+Var[Y] +Var[Z] %3D (observe that this also follows from the proposition on slide 5 of the lecture segment entitled "Binomial distribution").
