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(b) To fill an order for 100 units of a product, a firm wishes to distribute the production between its two plants, Plant 1 and Plant 2. The total cost function is given by
c=f(q_1,q_2 )=0.5q_1^2+2q_1+32q_2+500
where q_1 and q_2 are the number of units produced at Plants 1 and 2, respectively. How should the output be distributed in order to minimize costs?
c=f(q_1,q_2 )=0.5q_1^2+2q_1+32q_2+500
where q_1 and q_2 are the number of units produced at Plants 1 and 2, respectively. How should the output be distributed in order to minimize costs?
let Q={qi|x² + q²x + 4=0, q€N, x€R}. Find ⋃_(i=1)^∞▒Qi and ⋂_(i=1)^n▒Qi
a colony of ants carried away 26 of your muffins. that was 2/3 of them. how many are left?
A researcher wants to compare users of marijuana to users of crack cocaine to see if they differ in whether they are referred to drug courts after arrest. What type of statistical test should be used to conduct this analysis?
what is four and one third divided by 13
Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
(a) Suppose n = 36 and p = 0.23. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)
np =
nq =
, p̂ be approximated by a normal random variable because .
What are the values of μp̂ and σp̂? (Use 3 decimal places.)
μp̂ =
σp̂ =
(b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not?
, p̂ be approximated by a normal random variable because .
(c) Suppose n = 58 and p = 0.21. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)
np =
nq =
, p̂ be approximated by a normal random variable because .
What are the values of μp̂ and σp̂? (Use 3 decimal places.)
μp̂ =
σp̂ =
(a) Suppose n = 36 and p = 0.23. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)
np =
nq =
, p̂ be approximated by a normal random variable because .
What are the values of μp̂ and σp̂? (Use 3 decimal places.)
μp̂ =
σp̂ =
(b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not?
, p̂ be approximated by a normal random variable because .
(c) Suppose n = 58 and p = 0.21. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)
np =
nq =
, p̂ be approximated by a normal random variable because .
What are the values of μp̂ and σp̂? (Use 3 decimal places.)
μp̂ =
σp̂ =
4.5. Let (X,E) and (Y,K) be two measurable spaces.
We equip the product space X × Y with the σ-algebra σ(Xˆ).
Will a subset of X × Y of the form
A×Y, A∈E
be measurable?
Will a subset of the form
X×B, B∈K be measurable? Is Yˆ a measurable map?
We equip the product space X × Y with the σ-algebra σ(Xˆ).
Will a subset of X × Y of the form
A×Y, A∈E
be measurable?
Will a subset of the form
X×B, B∈K be measurable? Is Yˆ a measurable map?
4.4. Let (X1, E1), (X2, E2), (Y1, K1) and (Y2, K2) be measurable spaces.
Let
f1 : (X1,E1) → (Y1,K1), f2 : (X2,E2) → (Y2,K2), be measurable maps.
Construct the map f1 × f2 : X1 × X2 → Y1 × Y2 given by
f1 × f2 (x1, x2) = f1(x1), f2(x2) for all (x1, x2) ∈ X1 × X2
.
Show that f1 × f2 is E1 ⊗E2 −K1 ⊗K2 measurable.
Let
f1 : (X1,E1) → (Y1,K1), f2 : (X2,E2) → (Y2,K2), be measurable maps.
Construct the map f1 × f2 : X1 × X2 → Y1 × Y2 given by
f1 × f2 (x1, x2) = f1(x1), f2(x2) for all (x1, x2) ∈ X1 × X2
.
Show that f1 × f2 is E1 ⊗E2 −K1 ⊗K2 measurable.
A committee of 5 is to be formed from among 6 doctors, 5 CAs, 2 MBAs and 1 Government employee. Find the probability such that (i) each
profession is represented (ii) the committee has 1 Government employee and at least one MBA.
profession is represented (ii) the committee has 1 Government employee and at least one MBA.
Let O be the origin and OA = a1i + a2j + a3k. Find the equation of the plane that contains vectors I + j + k and 2i + j + k
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#340153 on Dec 2023
#340153 on Dec 2023