Maths TRB 2

If u and v are two independent Chi-square variables with r₁ and r₂ degrees of freedom, then the distribution of u + v is called

• Chi-square distribution

• t-distribution

• F-distribution

• Poisson distribution

The p.d.f. of a Chi-square distribution is

Finding the relation between two random variables is called

• regression

• analysis

• sample tests

• binomial

• Sampling

• Correlation

• Regression

• Analysis of variance

The arithmetic mean of Poisson distribution is

• λ²

• λ

• λ²/2

• λ'

A lot consists of 100 fuses. Five of these fuses are chosen at random and tested; if all 5 "blow" at the correct amperage, the lot is accepted. In fact, there are 20 defective fuses in the lot. Let the random variable X be the number of defective fuses among the 5 that are inspected. The random variable X is an example of

• Beta distribution

• Hypergeometric distribution

• Poisson distribution

• Gamma distribution

Let X₁, X₂ be a random sample of size n=2 from a standard normal distribution. Let Y₁=X₁/X₂ and Y₂=X₁+X₂. Now the marginal p.d.f. of Y₁ is that of a

• t-distribution

• F-distribution

• Chi-square distribution

• Poisson distribution

Let the random variable X have a distribution with finite variance σ² and mean μ. Then for every k>0, the Chebyshev's inequality is

• P(|X-μ| ≥ kσ) ≤ 1/k²

• P(|X-μ| ≥ kσ) ≤ k²

• P(|X-μ| ≥ kσ) ≥ 1/k²

• P(|X-μ| ≥ kσ) ≥ k²

Let X₁, X₂, ..., Xₙ denote the mean of a random sample of size n from a distribution that has mean μ and positive variance σ². Then Xₙ, n=1,2,3,... converges in probability to μ as n → ∞. This result is called the

• strong law of large numbers

• weak law of large numbers

• law of small numbers

• weak law of small numbers

Let X₁, X₂, ..., Xₙ denote the observations of a random sample from a distribution that has mean μ and positive variance σ². Then the Yₙ = (ΣXᵢ - nμ)/√nσ has a limiting distribution that is .......... with mean zero and variance 1.

• Multinomial

• Binomial

• Poisson

• Normal