Suppose the true average growth µ of one type of plant during a 1-year period is identical to that of a second type, but the variance of growth for the first type is s2, whereas for the second type, the variance is 4s2. let x1, x2, . . , xm be m independent growth observations on the first type (so e[xi] = µ, v [xi] = s2), and let y1, y2, . . , yn be n independent growth observations on the second type (so e[yi] = µ, v [yi] = 4s2).

a. show that for any d between 0 and 1, the estimator µˆ = dx ¯ + (1 - d)y ¯ is unbiased for µ.

b. for fixed m and n, compute v [µˆ], and then find the value of d that mini- mizes v [µˆ]. (hint: differentiate v [µˆ] with respect to d.)

you would need to know all the numbers that are on there

step-by-step explanation:

step-by-step explanation:

1/8 3/16 3/4

step-by-step explanation:

you put them as all the same denominator and multiply

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!