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- An automobile service facility specializing in engine tune-ups knows that 60% of all tune-ups are done on four-cylinder automobiles, 30% on six-cylinder automobiles, and 10% on eight-cylinder automobiles. Let X = the number of cylinders on the next car to be tuned. What is the pmf of X?An environmental engineer collected 10 moss and 10 lichen specimens. The engineer instructs a laboratory intern to randomly select 15 of the specimens. The probability mass function of the number of lichen specimens selected at random is: a) H (x; 15; 10; 20) b) P (x; 10) c) Bnegative (x, 10, 0.666) d) B (x, 10, 0.666)A fair coin is tossed three times and the random variable x equals the total number of heads. Find the sketch F(x) and f(x).
- If you flip a coin, there is a 1/2 chance you will receive a heads. If you flip a coin twice, you have to use the product rule to multiply each independent flip to find out what the odds of getting two heads in a row. (1/2 x 1/2=1/4.) By this rule, the odds of flipping a coin 13 times in a row twice and getting the exact same thing both times are 213. Mathematically, what are the chances that any two frog siblings will receive exactly the same complement of chromosomes due to random independent assortment (not counting random genetic recombination) Remember to add together the odds for both egg and sperm. What is this number for a human zygote? What does this tell you about the odds of being identical to one of your siblings, even without taking into account recombination (and not counting identical twins)?A medical researcher claims that the proportion of patients receiving 200 mg of a newly-developed influenza vaccine who go on to contract influenza strain X is less than the proportion of patients receiving 200 mg of last year's influenza vaccine who contract influenza strain X. Of 320 patients who are given last year's vaccine, 114 contract influenza strain X. Of 350 patients who are given the new vaccine, 112 of them contract influenza strain X. Let PN be the proportion of patients receiving the newly-developed vaccine and pL be the proportion of patients receiving last year's vaccine. State the null and alternative hypotheses and the value of the test statistic. Ho: PN =PL versus HA: PN > PL; Test statistic: Z = 0.99 Ho: PN=PL versus HA: PN > PL; Test statistic: Z = 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 0.99There are 2 players in a game. Each player independently picks a real number on the interval [0, 1] uniformly. If the (absolute) difference between the two numbers is less than a (0 < a < 1) and the sum of the two numbers is less than 1, then both players win, otherwise both players lose. What is the probability of winning? 2.
- Assume that W (t) is a standard Brownian motion and that S(t) is a random variable defined as S(t) = 8 · 2W(t). DetermineSuppose X-U (-54, 60) and F(t) is the cumulative distribution function. What is the probability that X is in the interval [-51, -21] or in the interval [-36, 57]? O (F(-21)-F(-51))+ (F(57) - F(-36)) O (F(-21)-F(-51)) x (F(57) - F(-36)) O F(-21)-F(-36) O F(57) - F(-51)Let X be a random variable and c be a constant. Then Var(X+c) = Var(X), always. True False
- In a public opinion survey, 60 out of a sample of 100 high income voters and 40 out of a sample of 75 low income voters supported a decrease in value added tax VAT. Conclude at the 5% level of significance that the proportion of voters favoring a VAT Degrees difference between high and low income voters. (Where P1 is the proportion of all high income voters who is supported a decrease in VAT, p2 is the same for the low income voters ). The value of the test statistic to test the hypothesis is _____ and hence _____ A. T = - 0.668,accept H0 B. T = - 4.117,reject H0 C. Z= 0.882,accept H0 D. T = 2.313,reject H0 E. Z = 0.882,reject H0Suppose 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 patientsA researcher selected a sample of 268 former student-athletes from a list of graduates of a large university. A total of 14% of the sample of athletes had earned graduate degrees as compared to 17% of all graduates. What is the Z obtained value?