For the scenario below, determine if the experiment describes a geometric distribution. If it is not a geometric setting, state why. if it is a geometric
a) the two outcomes
head or not head
b) What constitutes one trial
Flip a coin constitutes a flip coin
c) the probability of success
P(success) 1/2 or 50
Flip a coin until you observe a head.
1 year ago
1 year ago
a) Yes, the experiment describes a geometric distribution. The two outcomes of the experiment are "head" or "not head", which are the two possible outcomes for a coin flip.
b) One trial in this experiment is defined as flipping the coin once.
c) The probability of success in this experiment is 1/2 or 50%, because the probability of getting a head for a fair coin is 1/2.
Therefore, the experiment of flipping a coin until observing a head follows a geometric distribution, as it satisfies the necessary conditions for a geometric setting.
1 year ago
To determine if the given scenario describes a geometric distribution, we need to check if all the requirements for a geometric experiment are met.
a) The two outcomes: The experiment in this scenario has two outcomes, which are 'head' or 'not head'. This meets the first requirement of a geometric experiment.
b) What constitutes one trial: In this scenario, each time the coin is flipped is considered one trial. This meets the second requirement.
c) The probability of success: The probability of success, which is the probability of observing a head, is given as 1/2 or 0.5. This meets the third requirement.
Now, we can analyze the scenario based on the definition of a geometric distribution. A geometric distribution is a probability distribution that models the number of trials needed to achieve the first success in a sequence of independent Bernoulli trials, where each trial has the same probability of success.
In this scenario, the experiment involves flipping a coin until a head is observed. Each flip of the coin is considered a trial, and the probability of success (observing a head) is constant at 1/2.
Therefore, the given scenario does describe a geometric distribution because it meets all the requirements.