P(A1) = 0.22, P(A2) = 0.25, P(A3) = 0.28, P(A1 ∩ A2) = 0.14, P(A1 ∩ A3) = 0.04, P(A2 ∩ A3) = 0.07, P(A1 ∩ A2 ∩ A3) = 0.01.
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A computer consulting firm presently has bids out on three projects. Let Ai = {awarded project i}, for i = 1, 2, 3, and suppose that P(A1) = 0.22, P(A2) = 0.25, P(A3) = 0.28, P(A1 ∩ A2) = 0.14, P(A1 ∩ A3) = 0.04, P(A2 ∩ A3) = 0.07, P(A1 ∩ A2 ∩ A3) = 0.01. Express in words each of the following events, and compute the
(a) A1' ∩ A2' ∩ A3.
(b) (A1' ∩ A2') ∪ A3.
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- 4. Find the least-squares solution of Az = b for A = N and b = 2111. On the basis of her experience with clients, a clinical psychologist thinks that depression may affect sleep. She decides to test this idea. The sleep of nine depressed patients and eight normal controls is monitored for three consecutive nights. The average number of hours slept by each subject during the last two nights is shown in the following table: (Pagano, 2010). If proved significant, compute of the effect size. Hours of Sleep Depressed patients 7.1 Normal controls 8.2 6.8 7.5 6.7 7.3 7.7 7.8 7.5 8.0 6.2 7.4 6.9 7.3 6.5 6.5 7.2A 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= 0.99
- a production line is producing light bulbs. 90% of the bulbs are good and .10% are defective. Suppose each bulbls condition is dependent of the other bulbs condition Select three buls at randon: 1. P(all 3 are good)=? 2. P( 2 of 3 are good)= 3. P(1 of 3 are good)=A researcher wants to determine whether adolescents spend more time in a day around friends than adults do. He gathers a sample of n =10 adolescents (aged 12-17) and a sample of n =6 adults (aged 25-32). The researcher finds that the average time spent around friends for adolescents is M1= 3 hours with a SS1 of 44. He also finds that the average time spent around friends for adults is M2= 2 hours with a SS2 of 40. a. Do you use a one- or two-tailed test? What is the critical/cut-off t value with an alpha level of α = .01? b. What is the variance? c. What is the estimated standard error? d. What is the value of the t statistic? e. Do we reject or fail to reject the null hypothesis (α = .01)? Why? f. Calculate and report the variance explained ( r2)You work for an insurance company and are studying the relationship between types of crashes and the vehicles involved. As part of your study, you randomly select 3589 vehicle crashes and organize the resulting data as shown in the contigency table. At α=0.10, can you conclude that the type of crash depends on the type of vehicle? Complete parts (a) through (d). Vehicle Type of crash Car Pickup Sport utility Single-vehicle 866 323 340 Multiple-vehicle 1145 487 428 Question content area bottom Part 1 (a) Identify the claim and state the null and alternative hypotheses. H0: The type of crash and the type of vehicle are ▼ independent dependent . Ha: The type of crash and the type of vehicle are ▼ dependent independent . The ▼ alternative hypothesis null hypothesis is the claim.
- Q1. a) In the context of robot trajectories, state the difference between linear cartesian interpolation and joint interpolation. Give one example for each where one is more suitable than the other.Hydroxychloroquine is a drug sometimes used to treat malaria or rheumatoid arthritis. This drug has recently received some notoriety as a possible treatment for those suffering from Covid-19. A hydroxychloroquine tablet comes in a 200 mg strength, but hydroxychloroquine dosage may be anywhere from 200 to 1200 mg. Thus, a patient must take multiple pills. Suppose X is the number of pills taken by a randomly selected hydroxychloroquine patient. Then according to JJSDA, x has the following probability mass function, p(x), and cumulative distribution function F(x). 1 2 4 p(x) .04 .27 .35 .10 07 F(x) .04 .31 a .83 .93 1 a. If F is the cumulative distribution function of x, then what is the value of a? b. If p is the probability mass function for x, then evaluate b. c. What is the expected value of x? d. Calculate the variance of x. e. What is the variance of 0.7*x? f. The CDC 'randomly' checks the dosage of 10 hydroxychloroquine patients. What is the probability that exactly 4 of the…The subsets of {1,2} are Φ, {1}, {2} and {1,2}. So there are four possible potential models when deciding on a regression with a choice of inputs from a dataset containing two potential input variables. Your friend tells you this is nonsense and there are three possible models because the empty set Φ is just an imaginary concept concocted by some mathematician. What should you say to your friend? You should explain that the empty set corresponds to the model y = β + ε, where β is some constant and ε is a residual term. In this model, the output predictions are always equal to the output's sample average. You should explain that the empty set corresponds to the model y = ε, where ε is a residual term. In this model, the output predictions are totally random. You should indeed agree. Your friend is spot on and one cannot have a regression with no input variables. You should partially agree. Your friend is spot on that there are three models and not…
- I got the right calculations for p(x=0) and p(x=1) but I can’t seem to get 2,3, and 4 even though I’m using the same steps. Can you please show me where I’m making an error. Thank you!I need assistance with parts D, and EGiven the data points: (2,4), (?,8), (5,8), (6,5) and (17,4) , indicate In (y -Cs ) = Cz + Inx using Least Square Method. Note : For In (x) where x is a negative value, just write the expression and no need to evalu ate since In of a negative number is undefined.
