Titanic Here is a table we first saw in Chapter 2 showingwho survived the sinking of the Titanic based on whetherthey were crew members, or passengers booked in first-,second-, or third-class staterooms: a) If we draw an individual at random, what’s the prob-ability that we will draw a member of the crew? b) What’s the probability of randomly selecting a third-class passenger who survived? c) What’s the probability of a randomly selected passen-ger surviving, given that the passenger was a first-class passenger?d) If someone’s chances of surviving were the sameregardless of their status on the ship, how manymembers of the crew would you expect to havelived?e) State the null and alternative hypotheses.f) Give the degrees of freedom for the test.g) The chi-square value for the table is 187.8, and thecorresponding P-value is barely greater than 0. Stateyour conclusions about the hypotheses. Crew First Second Third TotalAlive 212 202 118 178 710Dead 673 123 167 528 1491Total 885 325 285 706 2201
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Titanic Here is a table we first saw in Chapter 2 showing
who survived the sinking of the Titanic based on whether
they were crew members, or passengers booked in first-,
second-, or third-class staterooms:
ability that we will draw a member of the crew?
class passenger who survived?
ger surviving, given that the passenger was a first-class
d) If someone’s chances of surviving were the same
regardless of their status on the ship, how many
members of the crew would you expect to have
lived?
e) State the null and alternative hypotheses.
f) Give the degrees of freedom for the test.
g) The chi-square value for the table is 187.8, and the
corresponding P-value is barely greater than 0. State
your conclusions about the hypotheses.
Alive 212 202 118 178 710
Dead 673 123 167 528 1491
Total 885 325 285 706 2201
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