We will then keep track of SCUICJ the meteorologist with the highest average score is the best predictor of weather. Suppose now that a given meteorologist is aware of this and so wants to maximize his or her expected score. If this individual truly believes that it will rain tomorrow with probability p*, what value of p should he or she assert so as to maximize the expected score? 24. An insurance company writes a policy to the effect that an amount must be paid if some event E occurs within a year. company estimates the E will occur within a year of money A If the with probability p, what should it charge the customer so that its expected profit will be 10 percent of A? 25. A total of 4 buses carrying 148 students from the same school arrive at a foorhall stadium. The buses carry, respectively, 40, 33, 25, and 50 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying this randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on her bus. (a) Which of E[X] or E[Y] do you think is larger? Why? (b) Compute E[X] and E[Y]. 26. Suppose that two teams play a series of games that end when one of them has won i games. Suppose that each game played is, independently, won by team A with probability p. Find the expected number of games that are played when i = 2. Also show that this number is maximized when p = ;. %3D %3D 2°
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.
Question 24
![We will then keep track of SCUICJ
the meteorologist with the highest average score is the best predictor of weather.
Suppose now that a given meteorologist is aware of this and so wants to maximize
his or her expected score. If this individual truly believes that it will rain tomorrow
with probability p*, what value of p should he or she assert so as to maximize the
expected score?
24. An insurance company writes a policy to the effect that an amount
must be paid if some event E occurs within a year. company estimates the
E will occur within a year
of
money A
If the
with probability p, what should it charge the customer
so that its expected profit will be 10 percent of A?
25. A total of 4 buses carrying 148 students from the same school arrive at a foorhall
stadium. The buses carry, respectively, 40, 33, 25, and 50 students. One of the
students is randomly selected. Let X denote the number of students that were on
the bus carrying this randomly selected student. One of the 4 bus drivers is also
randomly selected. Let Y denote the number of students on her bus.
(a) Which of E[X] or E[Y] do you think is larger? Why?
(b) Compute E[X] and E[Y].
26. Suppose that two teams play a series of games that end when one of them has won
i games. Suppose that each game played is, independently, won by team A with
probability p. Find the expected number of games that are played when i = 2.
Also show that this number is maximized when p = ;.
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