Probability and Statistics Quiz Quiz with Answet Key - Part 6

Criteria of selecting point estimator must include information of

• Consistency

• Efficiency

• unbiasedness

• all of above

Answer explanation

A good point estimator must be consistent, efficient, and unbiased. Consistency ensures it converges to the true parameter, efficiency means it has the smallest variance, and unbiasedness guarantees it hits the true parameter on average. Thus, the correct choice is 'all of above'.

If true value of population parameter is 10 and estimated value of population parameter is 15 then error of estimation is

• 5

• 0.667

• 25

• 150

Answer explanation

The error of estimation is calculated as the absolute difference between the true value (10) and the estimated value (15). Thus, |10 - 15| = 5, making the correct answer 5.

Way of getting information from measuring observation whose outcomes occurrence is on chance is called

• beta experiment

• alpha experiment

• random experiment

• gamma experiment

Answer explanation

A random experiment is a process of obtaining information through observations where the outcomes are uncertain and determined by chance. This distinguishes it from alpha, beta, and gamma experiments, which are not defined in this context.

Probability of second event in situation if first event has been occurred is classified as

• series probability

• joint probability

• conditional probability

• dependent probability

Answer explanation

The probability of the second event occurring given that the first event has already occurred is known as conditional probability. It reflects how the first event influences the likelihood of the second event.

In probability theories, events which can never occur together are classified as

• collectively exclusive events

• mutually exhaustive events

• mutually exclusive events

• collectively exhaustive events

Answer explanation

In probability, events that cannot occur simultaneously are called mutually exclusive events. This means if one event happens, the other cannot, making 'mutually exclusive events' the correct classification.

Joint probability of independent events J and K is equal to

• P(J) * P(K)

• P(J) + P(K)

• P(J) * P(K) + P(J-K)

• P(J) * P(K) - P(J * K)

Answer explanation

The joint probability of independent events J and K is calculated by multiplying their individual probabilities. Therefore, the correct answer is P(J) * P(K). The other options do not represent the correct relationship for independent events.

Variation in which outcomes of experiments are effected by uncontrolled factors is considered as

• random variation

• platykurtic variation

• mesokurtic variation

• mesokurtic variation

Answer explanation

Variation in outcomes due to uncontrolled factors is termed random variation. This type of variation is unpredictable and arises from inherent randomness in the experimental process, distinguishing it from other types of variation.

If two events X and Y are considered as partially overlapping events then rule of addition can be written as

• P(X or Y) = P(X) - P(Y) + P(X and Y)

• P(X or Y) = P(X) + P(Y) * P(X - Y)

• P(X or Y) = P(X) * P(Y) + P(X - Y)

• P(X or Y) = P(X) + P(Y) - P(X and Y)

Answer explanation

For partially overlapping events, the correct addition rule is P(X or Y) = P(X) + P(Y) - P(X and Y). This accounts for the overlap by subtracting the probability of both events occurring together.

If a person buys a lottery, chance of winning a Toyota car is 60%, chance of winning Hyundai car is 70% and chance of winning both is 40% then chance of winning Toyota or Hyundai is

• 0.6

• 0.8

• 0.9

• 0.5

Answer explanation

To find the chance of winning either a Toyota or Hyundai, use the formula: P(Toyota or Hyundai) = P(Toyota) + P(Hyundai) - P(Toyota and Hyundai). Thus, 0.6 + 0.7 - 0.4 = 0.9. Therefore, the correct answer is 0.9.

Types of probabilities for independent events must includes

• joint events

• conditional events

• marginal events

• all of above

Answer explanation

For independent events, probabilities include joint events (combined outcomes), conditional events (given one event occurs), and marginal events (individual probabilities). Thus, the correct answer is 'all of above'.