2–45. In problem 2–33, are “dividends paid” and “price increase” independent events? 2–33. An investment analyst collects data on stocks and notes whether or not dividends were paid and whether or not the stocks increased in price over a given period. Data are presented in the following table. Price No Price Increase Increase Total Dividends paid 34 78 112 No dividends paid 85 49 134 Total 119 127 246 a. If a stock is selected at random out of the analyst’s list of 246 stocks, what is the probability that it increased in price? b. If a stock is selected at random, what is the probability that it paid dividends? c. If a stock is randomly selected, what is the probability that it both increased in price and paid dividends? d. What is the probability that a randomly selected stock neither paid dividends nor increased in price? e. Given that a stock increased in price, what is the probability that it also paid dividends? f. If a stock is known not to have paid dividends, what is the probability that it increased in price? g. What is the probability that a randomly selected stock was worth holding during the period in question; that is, what is the probability that it increased in price or paid dividends or did both?
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.
2–45. In problem 2–33, are “dividends paid” and “price increase” independent
2–33. An investment analyst collects data on stocks and notes whether or not dividends were paid and whether or not the stocks increased in price over a given period. Data are presented in the following table. Price No Price Increase Increase Total Dividends paid 34 78 112 No dividends paid 85 49 134 Total 119 127 246 a. If a stock is selected at random out of the analyst’s list of 246 stocks, what is the
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