Various club have a game called the Big Six Money Wheel, which has 54 spaces in which are shown a Joker, the club logo, and distinctive dollar entireties, as exhibited in the table at the most elevated mark of the accompanying area. Players may bet on the Joker, the betting club logo, or possibly one dollar classes. The wheel is turned and if the wheel stops on a comparative put down as the player's bet, the player wins that entirety for each dollar bet.

Group Number of openings

$40 (Joker) 1

$40 (Casino logo) 1

$20 2

$10 4

$5 7

$2 15

$1 24

In case a player bets $5 on the $10 division, find the player's supposition. (Round your reaction to two decimal spots.)

Pick an American family erratically and request the number from TVs that family asserts. Here is the probability as directed by another survey:

Number of TVs 0 1 2 3

probability 0.10 0.44 0.28 0.18

What is the by and large expected number of TVs per family?

The gas cost consistently moves an uncommon game plan across different regions across country X. The going with data show the expense per gallon for standard gas for a self-assertive illustration of gas organization station for three huge brands of fuel (A, B and C) arranged in 10 metropolitan locales the country over X.

A B C

3.77 3.83 3.78

3.72 3.83 3.87

3.87 3.85 3.89

3.76 3.77 3.79

3.83 3.84 3.87

3.85 3.84 3.87

3.93 4.04 3.99

3.79 3.78 3.79

3.78 3.84 3.79

3.81 3.84 3.86

a. Express the invalid and elective hypothesis for single factor ANOVA to test for any basic differentiation in the mean expense of gas for the three brands.

b. Express the decision rule at 5% significance level.

c. Find out the test estimation.

d. Considering the decided test bits of knowledge pick whether any basic differentiation in the mean expense of gas for three gatherings.

The width of openings for connect saddle is known to have a standard deviation of 0.01 inches. A sporadic illustration of size

10 yields an ordinary distance across of 1.5045 inches. Use a 0.01 level of significance.

a. Test the hypothesis that the certifiable mean opening expansiveness approaches 1.50.

b. What is the P-an impetus for this test?

+11+

c. What size test would be imperative to perceive a real mean opening estimation of 1.505 slithers with a probability of at any rate

90%

d. What is the probability of presenting a sort 2 botch if the real width is 1.505 inches?

e. Find a 99% conviction length on the mean opening distance across..

Part I. From Bayesian Network to Full Joint Probability Distribution (12 points) Recall that a Bayesian network is a data structure for representing the full joint probability distribution. Given the following Bayesian network, where A = having allergy and S = Sneezing, compute the full joint probability table that the Bayesian network represents. A P(A) 0.] A S P(A.S) T T A P(S) T T 0.6 F T S F 0.3 F F1. Wallace's line is an imaginary biogeographic dividing line separating Asian fauna from those of Australasia named after Alfred Russell Wallace. This line runs predominantly between ... Sumatra and Java. Borneo and Sumatra. Mainland Asia and Sumatra. Australia and New Guinea. Borneo and Sulawesi. 2. The continental United States falls entirely within which of the following zoogeographic zones? Palearctic. Neotropical. Nearctic. Australian. Oriental.3. 1|.fll'hat has been the primary driver of faunal tumover during the Phanerozoic? II competitive displacement due to evolutionary arms race In competitive displacment due to changing environment I. competitive displacment due sexual selection In incumbent replacement after mass extinctions I. incumbent replacment due to evolutionaryr arms race 4. 1|.fll'hich of the following is a difference between a Bayesian approach to estimating a phylogenetic tree and a maximum likelihood approach? The Bayesian approach is restricted to only molecular data while the maximum likelihood approach may be used for either fossil data or molecular data. Only Bayesian approaches rely on a substitution model of molecular evolution as a starting point for estimating a phylogenetic tree from the data. Bayesian approaches to drawing phylogenetic inferences provide the probability of a particular tree given the data and some model of evolution while maximum likelihood methods provide the probability of the data given a particular tree and a model of evolution. Bayesian methods rely on distance methods and are therefore computationally easier to implement compared to maximum likelihood methods