1. Compute the sample standard deviation of the following data: x1 = 12,x2 = 7,x3 =...

1. Compute the sample standard deviation of the following data: x1 = 12,x2 = 7,x3 = 6,x4 = 8,x5 = 9.
A. ≈ 2.3 B. ≈ 2.6 C. ≈ 5.3 D. ≈ 6.8 E. other value
2. Suppose a simple random sample of size 16 from a normal population yields observed statistics of x¯ = 15.7 and s = 3.8. Find a 99% conﬁdence interval for the population mean µ.
A. [12.81,18.59] B. [12.9,18.50] C. [12.93,18.47] D. [13.25,18.15] E. other value
3. Suppose that of 300 people polled 225 of them say they plan retire by age 65. Find a (two-sided) 98% conﬁdence interval for number of people who plan to retire by age 65.
A. [.699,.802] B. [.696,.804] C. [.692,.808] D. [.686,.815]
4. How many people would you have to poll to be 97% sure that your margin of error will be less than 6%?
A. 328 B. 378 C. 543 D. 666 E. other value
The next three questions are based on the following data on the girth (in inches) and the height (in feet) of black cherry trees. Treat the girth as the independent/explanatory variable.
Girth 8.6 10.5 11.3 12.9 13.3 Height 65 72 79 85 86

Expert Solution

orchestra answered 1 year ago

Probabilities Compute P(X1 + 2X2 -2X3 > 7) , where X1, X2, X3 are iid random...

Probabilities Compute P(X1 + 2X2 -2X3 > 7) , where X1, X2, X3 are iid random variables with common distribution N(1,4). You must give the numerical answer. Specify and show any formulas used for E, P, and Var for example Var( X1 + 2X2 -2X3) = 4 + 22(4) + (-2)2(4) = 35. Please specify how all the individual numbers where obtained and the formula used.

The following table provides data for 20 samples each of size five. Sample x1 x2 x3...

The following table provides data for 20 samples each of size five. Sample x1 x2 x3 x4 x5 1 4.960 4.946 4.950 4.956 4.958 2 4.958 4.927 4.935 4.940 4.950 3 4.971 4.929 4.965 4.952 4.938 4 4.940 4.982 4.970 4.953 4.960 5 4.964 4.950 4.953 4.962 4.956 6 4.969 4.951 4.955 4.966 4.954 7 4.960 4.944 4.957 4.948 4.951 8 4.969 4.949 4.963 4.952 4.962 9 4.984 4.928 4.960 4.943 4.955 10 4.970 4.934 4.961 4.940 4.965 11 4.975...

Let X1, X2, X3 be independent having N(0,1). Let Y1=(X1-X2)/√2, Y2=(X1+X2-2*X3)/√6, Y3=(X1+X2+X3)/√3. Find the joint pdf...

Let X1, X2, X3 be independent having N(0,1). Let Y1=(X1-X2)/√2, Y2=(X1+X2-2*X3)/√6, Y3=(X1+X2+X3)/√3. Find the joint pdf of Y1, Y2, Y3, and the marginal pdfs.

4.Maximize: Z = 2X1+ X2-3X3 Subject to: 2X1+ X2= 14 X1+ X2+ X3≥6 X1, X2, X3≥0...

4.Maximize: Z = 2X1+ X2-3X3 Subject to: 2X1+ X2= 14 X1+ X2+ X3≥6 X1, X2, X3≥0 Solve the problem by using the M-technique.

(a) Consider three positive integers, x1, x2, x3, which satisfy the inequality below: x1 +x2 +x3...

(a) Consider three positive integers, x1, x2, x3, which satisfy the inequality below: x1 +x2 +x3 =17. (1) Let’s assume each element in the sample space (consisting of solution vectors (x1, x2, x3) satisfying the above conditions) is equally likely to occur. For example, we have equal chances to have (x1, x2, x3) = (1, 1, 15) or (x1, x2, x3) = (1, 2, 14). What is the probability the events x1 +x2 ≤8occurs,i.e.,P(x1 +x2 ≤8|x1 +x2 +x3 =17andx1,x2,x3 ∈Z+)(Z+...

Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if...

Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if 1<X1<2 -1<X2<0 -X2-1<X3<0 0 otherwise Find Cov(X2, X3)

#1 Compute the (sample) variance and standard deviation of the data sample. (Round your answers to...

#1 Compute the (sample) variance and standard deviation of the data sample. (Round your answers to two decimal places.) −1, 9, 9, 2, 11 variance standard deviation #2 Compute the (sample) variance and standard deviation of the data sample. (Round your answers to two decimal places.) −8, 3, 6, 8, 0, 6 variance standard deviation #3 Compute the (sample) variance and standard deviation of the data sample. (Round your answers to two decimal places.) 2.8, −3.2, 2.5, −0.2, −0.2 variance...

How do you simplify the following boolean expressions: Y3= X3' X2 X1 X0' + X3' X2...

How do you simplify the following boolean expressions: Y3= X3' X2 X1 X0' + X3' X2 X1 X0 + X3 X2 X1 X0' +X3X2X1X0 Y2 = X3' X2 X1' X0' + X3' X2 X1' X0 + X3 X2 X1' X0' + X3 X2 X1' X0 + X3 X2' X1' X0' + X3 X2' X1' X0 + X3 X2' X1 X0' + X3 X2' X1 X0 Y1 = X3' X2' X1 X0' + X3' X2' X1 X0 + X3' X2 X1 X0'...

Let X1,X2,X3 be i.i.d. N(0,1) random variables. Suppose Y1 = X1 + X2 + X3, Y2...

Let X1,X2,X3 be i.i.d. N(0,1) random variables. Suppose Y1 = X1 + X2 + X3, Y2 = X1 −X2, Y3 =X1 −X3. Find the joint pdf of Y = (Y1,Y2,Y3)′ using : Multivariate normal distribution properties.

Let X1, X2, X3, and X4 be a random sample of observations from a population with...

Let X1, X2, X3, and X4 be a random sample of observations from a population with mean ? and variance ?2. Consider the following two point estimators of ?: b1= 0.30 X1 + 0.30 X2 + 0.30 X3 + 0.30 X4 and b2= 0.20 X1 + 0.40 X2 + 0.40 X3 + 0.20 X4 . Which of the following constraints is true? A. Var(b1)/Var(b2)=0.76 B. Var(b1)Var(b2) C. Var(b1)=Var(b2) D. Var(b1)>Var(b2)

Question