Suppose that x has a Poisson distribution with μ = 2.

(b) Starting with the smallest possible value of x, calculate p(x) for each value of x until p(x) becomes smaller than .001. (Round your answers to 4 decimal places.)

(d) Find P(x = 2). (Round your answer to 4 decimal places.)

(e) Find P(x ≤ 4). (Round your answer to 4 decimal places.)

(f) Find P(x < 4). (Round your answer to 4 decimal places.)

(g) Find P(x ≥ 1) and P(x > 2). (Round your answers to 4 decimal places.)

(h) Find P(1 ≤ x ≤ 4). (Round your answer to 4 decimal places.)

(i) Find P(2 < x < 5). (Round your answer to 4 decimal places.)

(j) Find P(2 ≤ x < 6). (Round your answer to 4 decimal places.)

Suppose you are interested in estimating the relationship between edu (number of years of university education) and the inc (annual income measured in ten thousand) and you run the following regression: ??? = ?? + ?? ??? + ?

4.A Suppose ?? = ???? , ?? = ???? , ??? ? = 8. Further, if you know, ?̅ = 3.2125, ?̅= 25.875, ∑ (?? − ?̅ ? ?=1 ) (?? − ?̅) = 5.8125 and ∑ (?? − ?̅) 2 = 56.875 ? ?=1 , calculate the value of the parameter ?2.

4.B Based on the information in 4.A and value of ?2 you computed, calculate the value of the intercept ?1. Please show all the calculation step by step.

4.C According to your parameter estimates, what is the predicted value of inc when edu = 20?

4.D If the sum of the residuals of squares, ∑ ?? 2 = 0.2247 ? ?=1 and the total sum of squares, ∑ (?? − ?̅) 2 = 1.0288 ? ?=1 , can you calculate the ? 2 ? Please show the calculation and make sure to interpret the result.

A sample of nurses with affiliation to private hospitals (affiliation = 0) and to university hospitals (affiliation = 1) was asked to rate their confidence in making the right decisions based on their level of ongoing inservice professional development. Use a Mann-Whitney U-test to determine if the distribution of confidence in each group is the same. The file is the first tab in “nonparametric.xlsx.”

Be sure to always write the null and alternate hypotheses, so that the decision is made in the correct direction. Also, conduct all as two-tailed tests at α = 0.05.

About finding the number of permutations

Let there be n pairs of 2*n students : (1, 2) , (3, 4), (5, 6) ... (2n-1 , 2n). We want to find the number of arrangements of students which the pair are not adjacent. In other words, for (2*i) th student, the (2*i -1) th student should not be in his front or back.

For example, think of case of n=2. In this case, (1, 4, 3, 2) is not appropriate for this question because 4 and 3 are adjacent although they are pair. So we must count arrangements such as (1, 3, 2, 4)... etc for n=2

Let such total cases to be B_n. In this situation, how can we calculate the limit of (B_n)/ (2n!) ?

1) Find the exact absolute max and exact min for f(x)=x^3-3x^2-6x+4 on the closed interval [0,3]

2) Let f be continuously differentiable function on the Reals with the following characteristics:

- f(x) is increasing from intervals (0,2) and (4,5) and decreasing everywhere else

- f(x) > -1 on the interval (1,3) and f(x) < -1 everywhere else

Suppose g(x) = 2f(x) + (f(x))^2. On which interval(s) is g(x) increasing?

Differentiate the following:

1) f(x) = √2x-4. (all under square root)

2) f(x) = x/5-x

3) y=cos(4x^3)

4) f(x)=tan(x^2)

5) f(x)= 3e^2x cos(2x)

6) y= sin2x/cosx

7) y= √sin(cosx) (all under the square root)

Chromatography Terms

1.Transmittance

2.Emission

3. Fluorescne

4. phosphorescnce

5. Line spectrum

6. Ground state

7. Excitd state

8. Path Length

9.Moar Absorptivity

10. coherent Radiation

11. Monochrometer

12. Diffraction Grating

For the following probability mass function, p(x)=1/x for x=2, 4, 8 p(x) = k/x2 for x=16 Find the value of k. Find the standard deviation of (7-9X).