In the carnival game chuck-a-luck, three dice are rolled. You make a bet on a particular number (1, 2, 3, 4, 5, 6) showing up. The payout is 1 to 1 if that number shows on (exactly) one die, 2 to 1 if it shows on two dice, and 3 to 1 if it shows up on all three. (You lose your initial stake if your number does not show on any of the dice.) If you make a $1 bet on the number three, what is your expected net winnings? (answer to 3 decimal places)

Consider the following differential equation:

(t^2)y'-y=(y^2), where y'=dy/dt.

(a) find y(t) if y(1)=1/2

(b)find lim_t->infinityy(t)

Construct a derivation (for the following argument) from the premise to the conclusion, only using these :(&I, &E, ∨I, ∨E, ≡ I, ≡ E ,⊃ I, ⊃ E,∼ I, ∼ E)

(a) Premise 1: W ⊃ X

     Premise 2: X ⊃ Y

     Premise 3: Y ⊃ Z

     Premise 4: W

    Conclusion: W & Z

(b)Premise 1: (A & B) ≡ C

    Premise 2: A ≡ B

   Conclusion: A ≡ C

(c)Premise 1: B ⊃ D

Premise 2: C ⊃ D

Conclusion: (B ∨ C) ⊃ D

(d) Premise 1: B ⊃ C

Conclusion: ∼ C ⊃∼ B

There are two identical, positively charged conducting spheres fixed in space. The spheres are 34.8 cm apart (center to center) and repel each other with an electrostatic force of ?1=0.0765 N . A thin conducting wire connects the spheres, redistributing the charge on each sphere. When the wire is removed, the spheres still repel, but with a force of ?2=0.100 N . The Coulomb force constant is ?=1/(4??0)=8.99×109 N⋅m2/C2 . Using this information, find the initial charge on each sphere, ?1 and ?2 , if ?1 is initially less than ?2 . find q1 and q2.

Use Java for the following;

Part 1

n!= n * (n –1)* (n–2)* ...* 3 * 2 * 1

For example, 5! = 5 * 4 * 3 * 2 * 1 = 120

Write a function called factorial that takes as input an integer. Your function should verify that the input is positive (i.e. it is greater than 0). Then, it should compute the value of the factorial using a for loop and return the value. In main, display a table of the integers from 0 to 30 along with their factorials. At some point around 15, you will probably see that the answers are not correct anymore. Think about why this is happening.

Run the following analyses using R.

Thirty-six Midwestern junior high students were randomly selected to participate in a study about the effectiveness of six different math curricula. The researcher randomly assigned six students to each of the six conditions (n_j = 6 for all groups). At the end of a lesson on fractions, students were administered a 10-point quiz. Each student’s score is in the table below:

1. Perform a one-way ANOVA of these data by completing the following table:

Table 1. ANOVA Summary Table

Is the omnibus F test statistically significant at the a = 0.05 level? How should the researcher interpret this result?

2. The researcher is interested in testing the differences among all of the pairs of means.
   1. How many such unique pairwise comparisons are possible?
   2. Conduct an t-test for each of these comparisons.
   3. Which t-tests from question are significant without doing any adjustments (based on an a level = 0.05 for each t test)?

3. The researcher worries about the possible Type I Error associated with doing this many tests, and therefore wants to make adjustments.
   1. Use Bonferroni adjustment
   2. Use Holm-Bonferroni adjustment
   3. Use Fisher’s LSD test
   4. Use Tukey’s HSD Test
   5. Which post hoc test will you choose to use and why?
   6. Based on the result of the post hoc test you chose, which group means were found to be significantly different?

If X is a random variable with the given distribution, determine – without calculations! – which of the two probabilities is higher or if they have to be equal. Explain your answer.

(a) P{−1 6 X 6 4} and P{10 6 X 6 15}, where X ∼ Uniform(−10, 20).

(b) P{−1 6 X 6 4} and P{10 6 X 6 15}, where X ∼ Normal(2, 3).

Of the two officers selected from a group of officers, the probability of the first being male and the second being female is 1/4. Since the ratio of male civil servants to female civil servants is 1/2, how many civil servants are there in the group? b) One bag contains 6 white and 4 black balls. What is the probability that one of the 3 balls drawn randomly from this bag is white and the other two are black?

Q.2. The following frequency distribution summarizes the weights of 200 garlands made in a shop. Weight (kgs) 1-3 4-6 7-9 10-12 Frequency 53 118 21 8 Calculate the mean, median and standard deviation of these data.

Calculate the mean, median and standard deviation of these data.

1. Using excel, determine:

1. The present value of a five (5) year project, with expected annual cash flows given below, assuming the cost of capital of 12.5% p.a.                                                                (1 Mark)

ii. The future value of $ 12,200 received annually over a period of four (4) years, interest paid quarterly at the rate of 14% p.a.