what is the probability?

A jar contains 4 red marbles, numbered 1 to 4, and 12 blue marbles numbered 1 to 12.

a) A marble is chosen at random. If you’re told the marble is blue, what is the probability that it has the number 2 on it?

b) The first marble is replaced, and another marble is chosen at random. If you’re told the marble has the number 1 on it, what is the probability the marble is blue?

Unit 4: Discussion - Part 1

Question

Read the lecture for Chapter 4, and then answer the following:

Think of a brief example where you can use conditional statements and write it in correct Java syntax. You may use if-else-if statements or the switch statement. You may also use the example you wrote in pseudo code for the discussion thread 2 during week 2 and convert it to Java, if you think it is appropriate. Be mindful that we are not talking about homework here. Do not post homework in this or any other discussion thread. As always, show a screen capture of the program running.
After writing your example, please explain if you think your example could also be written in the other conditional statement you did not chose. Explain why you think so, or why not.

1. Design the logic for a program that outputs every multiple of 4, from 4 through 100
along with its value squared and cubed, e.g.,
The next number: 4
Squared: 16
Cubed: 64
The next number: 8
Squared: 64
Cubed: 512

Gasoline mileage (mpg) was measured on several cars of each of four different makes (coded 1, 2, 3 and 4). The make of each car is stored in the first column, and the mileage for each car is stored in the second column, of Table A. You need to conduct an analysis of variance to see if there are differences among the four makes in gasoline mileage. You should also estimate the mileage of each of the four makes of cars.
1. What is the value of the F‑statistic for testing the null hypothesis that there are no differences in gasoline mileage among the four makes of automobile?
2. What are the degrees of freedom associated with the numerator of this test statistic?
3. What are the degrees of freedom associated with the denominator of the F‑value for MAKE of car?
4. What is the estimate of the pooled variance within makes of cars (i.e. the Error mean square)?
5. What are the degrees of freedom for this variance in #4?

Is there a statistically significant difference in mean scores between any of the following groups? Calculate and report the mean for each group. If one or more mean differences exist, please identify the groups with significantly different means. Use the most appropriate statistical test to answer this question at the alpha = 0.05 level of significance. Identify the hypothesis statements, test statistic, p-value, and your decision.

Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2, 3}, and transition probability matrix (pij ) given by   2 3 1 3 0 0 1 3 2 3 0 0 0 1 4 1 4 1 2 0 0 1 2 1 2   Determine all recurrent states. Q3. Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2} and transition probability matrix (pij ) given by   2 3 1 3 0 1 3 2 3 0 0 1 4 3 4   Determine all transient states. Q4. Classify the states {1, 2, 3} of the Markov chain with transition matrix   1 3 1 3 1 3 1 2 0 1 2 2 3 0 1 3 

Test for correlation between Barley and Corn prices using Spearman's rank correlation method, at the 0.05 significance level.

The statement of financial position of Swifty Corporation follows for the current year, 2020:

The following additional information is available:

(a)

Prepare a statement of financial position in good form. (Adjust the amounts in each SFP classification based on the additional information.)

1. For each permutationσ of {1,2,··· ,6} write the permutation matrix M(σ) and compute the determinant |m(σ)|, which equals sgn(σ).

(a) The permutation given by 1 → 2, 2 → 4, 3 → 3, 4 → 1, 5 → 6, 6 → 5.

(b)  The permutation given by 1 → 5, 2 → 1, 3 → 2, 4 → 6, 5 → 3, 6 → 4.

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