Podcast
Questions and Answers
What type of probability distribution does the random variable X follow?
What type of probability distribution does the random variable X follow?
- Uniform distribution
- Normal distribution (correct)
- Binomial distribution
- Poisson distribution
What are the parameters of the normal distribution for the random variable X?
What are the parameters of the normal distribution for the random variable X?
- Mean = 1, Standard deviation = 1
- Mean = 0, Standard deviation = 0
- Mean = 1, Standard deviation = 0
- Mean = 0, Standard deviation = 1 (correct)
In $P(X \geq S) = 0.05$, what does S represent?
In $P(X \geq S) = 0.05$, what does S represent?
- The mean of X
- The standard deviation of X
- A threshold value (correct)
- The probability that X is less than S
What does $P(X \geq S)$ represent in the context of the problem?
What does $P(X \geq S)$ represent in the context of the problem?
If $P(X \geq S) = 0.05$, what is the value of $P(X < S)$?
If $P(X \geq S) = 0.05$, what is the value of $P(X < S)$?
What is the significance of determining the value of S?
What is the significance of determining the value of S?
What is assessed to be 0.05?
What is assessed to be 0.05?
What does X represent in the context?
What does X represent in the context?
Which country was losing before winning at the end of the match?
Which country was losing before winning at the end of the match?
What event is considered improbable?
What event is considered improbable?
Flashcards
X in the context of the match?
X in the context of the match?
A random variable following a standard normal distribution, modeling the probability of a comeback at the end of a match.
What is the value of S?
What is the value of S?
The threshold value S such that the probability of the random variable X being greater than or equal to S is 0.05, representing a highly improbable equalization.
Victory unexpectedly?
Victory unexpectedly?
Given the equalization occurs, the probability of winning the match in extra time follows a standard normal distribution with a probability of P(X≥T) = 0.6.
What is determine the threshold T
What is determine the threshold T
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Study Notes
- The exercise involves "An Extraordinary Comeback!".
- During the quarter-final of the CAN 2023 between Côte d'Ivoire and Mali, Côte d'Ivoire was behind until the 89th minute and 17 seconds but eventually won the match.
- A random variable X follows a standard normal distribution, denoted as X ~ N(0, 1).
- X models the probability of a turnaround in the situation at the end of the match.
- The probability of equalizing after 89 minutes and 17 seconds is considered improbable.
- It's estimated that the probability of X being greater than or equal to a threshold value S is 0.05, or P(X ≥ S) = 0.05.
- Determine the value of S and interpret this probability in the context of the match.
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