C955 Applied Probability and Statistics - Set 1 - Part 3

Correct Answer: 1/4

There are 13 hearts among 52 cards, giving 13/52, which simplifies to 1/4.

Correct Answer: 1/13

There are 4 aces among 52 cards, giving 4/52, which simplifies to 1/13.

Correct Answer: A variable taking countable distinct values

A discrete random variable takes separate countable values, such as the number of defects, whereas a continuous variable can take any value in a range.

Correct Answer: The height of a randomly selected adult

Height can take any value within a range and is measured rather than counted, making it continuous. The others are counts and therefore discrete.

Correct Answer: Each is between 0 and 1 and they sum to 1

Every probability must lie between 0 and 1 inclusive, and the probabilities of all possible outcomes must total exactly 1.

Correct Answer: The long-run average value, computed as the sum of each value times its probability

Expected value is a probability-weighted average representing the long-run mean over many repetitions, and it need not equal any actual attainable outcome.

Correct Answer: $2

Expected value equals (10 times 0.2) plus (0 times 0.8), which is 2 plus 0, giving $2.

Correct Answer: Fixed number of independent trials, two outcomes, constant probability

A binomial setting requires a fixed number of trials, two possible outcomes per trial, independent trials, and the same success probability throughout.

Correct Answer: n times p

The mean number of successes in a binomial distribution equals the number of trials multiplied by the probability of success on each trial.

Correct Answer: 10

Using the binomial mean n times p, the expectation is 20 multiplied by 0.5, which equals 10.