National Statistics Day 2024

1. Which distribution is appropriate for modelling the number of arrivals at a service point in a given period of time?

• Binomial distribution

• Normal distribution

• Poisson distribution

• Uniform distribution

1. The Spearman rank correlation coefficient is used when:

• The data are normally distributed.

• The relationship between variables is linear.

• The data are ordinal.

• There are no ties in the data.

1. If two events A and B are mutually exclusive, what is the probability of both events occurring together?

• P(A) + P(B)

• P(A) * P(B)

• P(A) + P(B) - P(A ∩ B)

• 0

• Var(Y)

• 0

1. Which of the following values of Karl Pearson's correlation coefficient indicates the strongest linear relationship?

• 0.8

• -0.9

• 0

• 0.3

1. Which of the following statements is true about a distribution with a positive skewness?

• The right tail is longer than the left tail.

• The left tail is longer than the right tail.

• The distribution is symmetric.

• The distribution has a high peak.

1. Which of the following scenarios can be modelled using the hypergeometric distribution?

• Drawing balls from an urn with replacement.

• The number of successes in a sequence of independent trials.

• Selecting a sample of defective items from a batch of products without replacement.

• The number of arrivals at a service center.

1. Let X₁​,X₂​,…,X_n​ be i.i.d. Bernoulli random variables with parameter p. According to Bernoulli’s law of large numbers, the sample mean  converges to:

• p

• 0

• 1

• 1/n

1. If two random variables X and Y have a covariance of zero, which of the following statements is true?

• X and Y are independent.

• X and Y have no linear relationship.

• X and Y have the same variance.

• X and Y have a correlation coefficient of 1.

1. For an Exponential distribution with parameter θ,

•   0<θ<∞

• 0<θ<1

• -∞<θ<∞

• None of these