Methods of Estimation MCQ Quiz in मल्याळम - Objective Question with Answer for Methods of Estimation - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Last updated on Apr 4, 2025

നേടുക Methods of Estimation ഉത്തരങ്ങളും വിശദമായ പരിഹാരങ്ങളുമുള്ള മൾട്ടിപ്പിൾ ചോയ്സ് ചോദ്യങ്ങൾ (MCQ ക്വിസ്). ഇവ സൗജന്യമായി ഡൗൺലോഡ് ചെയ്യുക Methods of Estimation MCQ ക്വിസ് പിഡിഎഫ്, ബാങ്കിംഗ്, എസ്എസ്‌സി, റെയിൽവേ, യുപിഎസ്‌സി, സ്റ്റേറ്റ് പിഎസ്‌സി തുടങ്ങിയ നിങ്ങളുടെ വരാനിരിക്കുന്ന പരീക്ഷകൾക്കായി തയ്യാറെടുക്കുക

Latest Methods of Estimation MCQ Objective Questions

Top Methods of Estimation MCQ Objective Questions

Methods of Estimation Question 1:

Consider the multiple linear regression model

Yi = β1xi1 + ..., + βpxip + ϵi, with E(ϵi) = 0, Cov (ϵi, ϵk) = 0, if i ≠ k and Var (ϵi) = σ2, for i, k = 1, ..., n.

If yi^ is the least squares fit of yi and ϵi^, is the corresponding estimated residual for i = 1, ..., n, then which of the following statements are always correct?

  1. iϵ^i=0 and iy^iϵ^l=0.
  2. ixijϵ^i=0; for all j = 1, ..., p.
  3. iϵ^i=0 and ixijϵ^l=0;  for all j = 1, ..., p
  4. iy^lϵ^l=0

Answer (Detailed Solution Below)

Option :

Methods of Estimation Question 1 Detailed Solution

The correct answer are option 2 & 4 

we will update the solution as soon as possible.

Methods of Estimation Question 2:

For a given bivariate data (yi, xi), i = 1, ..., n, Analyst A fits Y on X, i.e., Y^i=α0^+α1^xi, while Analyst B fits X on Y, i.e., X^i=β0^+β1^yi, using the ordinary least squares estimation method. Which of the following pairs is a possible value for (α^1,β^1) ?

  1. (-0.5, 2.5)
  2. (0.5, 2.5)
  3. (-2.0, 0.4)
  4. (-2.0, -0.4)

Answer (Detailed Solution Below)

Option 4 : (-2.0, -0.4)

Methods of Estimation Question 2 Detailed Solution

The correct answer is option 4 

we will update the solution as soon as possible.

Methods of Estimation Question 3:

Given the observations 0.8, 0.71, 0.9, 1.2, 1.68, 1.4, 0.88, 1.62 from the uniform distribution on (θ - 0.2, θ + 0.8) with -∞ < θ < ∞, which of the following is a maximum likelihood estimate for θ? 

  1. 0.7
  2. 0.9
  3. 1.1
  4. 1.3

Answer (Detailed Solution Below)

Option :

Methods of Estimation Question 3 Detailed Solution

Maximum likelihood estimate for θ is 0.9

(2) is correct

Methods of Estimation Question 4:

Let X1, X2, ..., Xn be a random sample from the distribution with p.d.f.

\(\rm f_θ(x)=\left\{\begin{array}{cc} \frac{1}{θ} \cdot x^{\frac{1-θ}{θ}}, & 0

where θ > 0. Then which of the following are true? 

  1. i=1nXi is sufficient for θ.
  2. 1ni=1nlnXi is sufficient for θ.
  3. i=1nXi is a maximum likelihood estimate for θ.
  4. 1ni=1nlnXi is a maximum likelihood estimate for θ.

Answer (Detailed Solution Below)

Option :

Methods of Estimation Question 4 Detailed Solution

The Correct Answer is Option 1, 2 & 4

Methods of Estimation Question 5:

Consider a linear model Y4×1 = X4×4β4×1 + ε4×1, where Disp(ε) σ2I4 for some σ> 0. One needs to choose the design matrix X such that its elements take values in the set {-1, 0, 1}. Now, consider the following three choices of X  

X1=[1000010000100001],

X2=[1100110000110011] and

X3=[1111111111111111].

Which of the following statements are true? 

  1. For all three choices of X, β = (β1, β2, β3, β4)' is estimable
  2. For all three choices of X, β^i, and βj^, the least squared estimates of βi and βj, are uncorrelated for all i ≠ j
  3. X2 is a better choice than X1  
  4. X2 is a better choice than X3

Answer (Detailed Solution Below)

Option :

Methods of Estimation Question 5 Detailed Solution

For all three choices of X, β = (β1, β2, β3, β4)' is estimable

For all three choices of X, β^i, and βj^, the least squared estimates of βi and βj, are uncorrelated for all i ≠ j

X2 is a better choice than X1  

(1), (2), (3) are correct

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