Modeling Process Quality -Continuous Distributions MCQ

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• The rule of multiplication of probability is possible only _____________
  ক

  When events are independent

  খ

  When events are mutually exclusive

  গ

  When events are Bayesian

  ঘ

  When events are Empirical
• If a card is chosen from a deck of cards, what is the probability that it is either 7 or 9?
  ক

  4/52

  খ

  7/52

  গ

  9/52

  ঘ

  8/52
• The cumulative distribution function for the lognormal distribution is given by _____ \) b) \(\phi\) c) \(\phi\) d) \(\phi\)
  ক

  \(\phi-\theta}{\omega}]\) \) c) \(\phi-\omega}{\omega}]\) d) \(\phi-\theta}{\theta}]\) View Answer]

  খ

  \frac{ln⁡(a)-\theta}{\omega}

  গ

  \frac{ln⁡(a)-\theta}{\omega}

  ঘ

  \frac{ln⁡(a)-\theta}{\omega}
• The exponential distribution is given by _____
  ক

  f(x)=xeλ

  খ

  f(x)= e-λx

  গ

  f(x)= λe-λx

  ঘ

  f(x)=ew
• For a lognormal random variable, what is the value of mean?
  ক

  \(μ=e^{\theta+\frac{w^2}{2}}\)

  খ

  \(μ=e^{\frac{w^2+\theta}{2}}\)

  গ

  \(μ=e^{w+\frac{\theta^2}{2}}\)

  ঘ

  \(μ=e^{\theta+w^2}\)
• If a variable x is having its value equal to the exponential function of another variable w, i.e. “x=exp⁡(w)”, and w has normal distribution; the distribution of x is called _______
  ক

  Normal distribution

  খ

  Exponential distribution

  গ

  Lognormal distribution

  ঘ

  Gamma distribution
• The central limit theorem is true for _______ distribution.
  ক

  Normal distribution

  খ

  Lognormal distribution

  গ

  Exponential distribution

  ঘ

  Gamma distribution
• Which of these is true for the normal distributions?
  ক

  \(μ_y = a_1 μ_1 + a_2 μ_2 +⋯+ a_n μ_n\)

  খ

  \(μ_y = a_1 μ_1^2 + a_2 μ_2^2 +⋯+ a_n μ_n^2\)

  গ

  \(μ_y^2 = a_1^2 μ_1^2 + a_2^2 μ_2^2 +⋯+ a_n^2 μ_n^2\)

  ঘ

  \(σ_y^2 = a_1^2 σ_1^2 + a_2^2 σ_2^2 +⋯+ a_n^2 σ_n^2\)
• The probability that the normal random variable x is less than or equal to some value a is said to be the _____
  ক

  Standard normal distribution

  খ

  Lognormal distribution

  গ

  Exponential distribution

  ঘ

  Cumulative normal distribution
• “ϕ(∙)” is said to be cumulative distribution function of _________
  ক

  Standard binomial distribution

  খ

  Standard normal distribution

  গ

  Standard exponential distribution

  ঘ

  Standard gamma distribution
• The rule of multiplication of probability is possible only ____
  ক

  When events are independent

  খ

  When events are mutually exclusive

  গ

  When events are Bayesian

  ঘ

  When events are Empirical
• Which of these distributions has an appearance of bell-shaped or unimodal curve?
  ক

  Lognormal distributions

  খ

  Normal distribution

  গ

  Exponential distribution

  ঘ

  Cumulative exponential distributions
• Which of these is a continuous distribution?
  ক

  Pascal distribution

  খ

  Lognormal distribution

  গ

  Binomial distribution

  ঘ

  Hyper geometric distribution
• Which of these cannot be shown on the continuous distributions?
  ক

  Length dimension measurement of a box

  খ

  Volume measurement of the box

  গ

  Area measurement of one face of the box

  ঘ

  Number of defects on the surface of the box