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How do you give the probability of a sum?
You find the event space for the random variable that is the required sum and then calculate the probabilities of each favourable outcome. In the simplest case it is a convolution of the probability distribution functions.
What re the three criteria needed for something to be a probability distribution?
A probability distribution must have a well defined domain - that is, the set of possible outcomes.For each possible outcome, there must be a non-negative value associated - the probability of that outcome.The sum of the probabilities, over all possible outcomes, must be 1.
John will toss a coin three times What is the probability that the coin will land heads up all 3 times?
(0.5)*(0.5)*(0.5) = 0.125 or 12.5% Please note the following in computing probabilities: Each toss is an independent event, the result of one toss does not affect the outcome of the next. The only outcomes are heads and tails. The probability of either outcome is 0.50 and does not change. Also note that many problems in real life are unlike coin flips, events are dependent on each other, outcomes are numerous, and not easily assigned probabilities. This does not necessarily make calculation of probabilities impossible, only more complicated.
What is a probability distribution?
A probability distribution is a function that describes the probability of obtaining a certain outcome where the outcomes are not equally likely. There is a fixed probability of getting each outcome, but the probabilities are not necessarily equal. For example, roll 2 dice, there are 36 equally likely outcomes with a probability of each occurring being 1/36. However if we look at the sum of the numbers, there is only one outcome that gives a sum of 2 (1&1) , so P(sum 2) = 1/36, but six outcomes that give the sum of 7 (1&6, 2&5, 3&4, 4&3, 5&2, 6&1), so P(sum 7) = 6/36 = 1/6. Probability distributions can be tabulated, or there are functions that can be used to calculate the probabilities of getting each outcome. A probability distribution is a function that describes the probability of obtaining a certain outcome where the outcomes are not equally likely. There is a fixed probability of getting each outcome, but the probabilities are not necessarily equal. For example, roll 2 dice, there are 36 equally likely outcomes with a probability of each occurring being 1/36. However if we look at the sum of the numbers, there is only one outcome that gives a sum of 2 (1&1) , so P(sum 2) = 1/36, but six outcomes that give the sum of 7 (1&6, 2&5, 3&4, 4&3, 5&2, 6&1), so P(sum 7) = 6/36 = 1/6. Probability distributions can be tabulated, or there are functions that can be used to calculate the probabilities of getting each outcome.
What is meant by probability distribution?
I will give first the non-mathematical definition as given by Triola in Elementary Statistics: A random variable is a variable typicaly represented by x that has a a single numerical value, determined by chance for each outcome of a procedure. A probability distribution is a graph, table or formula that gives the probabability for each value of the random variable. A mathematical definition given by DeGroot in "Probability and Statistics" A real valued function that is defined in space S is called a random variable. For each random variable X and each set A of real numbers, we could calculate the probabilities. The collection of all of these probabilities is the distribution of X. Triola gets accross the idea of a collection as a table, graph or formula. Further to the definition is the types of distributions- discrete or continuous. Some well know distribution are the normal distribution, exponential, binomial, uniform, triangular and Poisson.
When two probabilities are multiplied the probability represents a compound event true or false?
True. When two probabilities are multiplied, it represents the probability of a compound event occurring, specifically when the two events are independent. This means the outcome of one event does not affect the outcome of the other. For example, the probability of rolling a certain number on a die and flipping a coin simultaneously can be found by multiplying the individual probabilities of each event.
What is the relationship between expected value and probability in decision-making processes?
Expected value is a measure of the average outcome of a decision, calculated by multiplying the probability of each possible outcome by the value of that outcome. In decision-making, the expected value helps to assess the potential outcomes of different choices based on their probabilities, allowing individuals to make informed decisions by considering both the likelihood of different outcomes and their associated values.
What does nonreplacement mean in probability?
It refers to experiments where more than one tokens are randomly selected from a set of tokens (of different colours). If the the token is replaced after each selection, the probabilities remain constant whereas if the token is not replaced - as the question suggests - the probabilities change, depending on the outcome of the selection.It refers to experiments where more than one tokens are randomly selected from a set of tokens (of different colours). If the the token is replaced after each selection, the probabilities remain constant whereas if the token is not replaced - as the question suggests - the probabilities change, depending on the outcome of the selection.It refers to experiments where more than one tokens are randomly selected from a set of tokens (of different colours). If the the token is replaced after each selection, the probabilities remain constant whereas if the token is not replaced - as the question suggests - the probabilities change, depending on the outcome of the selection.It refers to experiments where more than one tokens are randomly selected from a set of tokens (of different colours). If the the token is replaced after each selection, the probabilities remain constant whereas if the token is not replaced - as the question suggests - the probabilities change, depending on the outcome of the selection.
What is the definition of expected outcome?
The expected outcome of an experiment, where the outcomes have discrete values, is the sum of the values of each outcome multiplied by the probability of that value occurring. For continuous variables, it is the integral of each value multiplied by the probability of that value being attained. The expected value for a variable is the [arithmetic] mean for that variable. Note, though, that the arithmetic mean may be unrealisable. For example, the expected value for the roll of a fair die is 1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6) = 21/6 = 31/2. And no matter how hard you try, you will not roll 31/2! What the expected value says is that, if you roll the die many times, the average of all the values that you get will be approximately 31/2.
How can one determine the mixed strategy Nash equilibrium in a game?
To determine the mixed strategy Nash equilibrium in a game, one must calculate the probabilities that each player will choose their strategies. This involves finding the best response for each player given the probabilities of the other player's strategies. The mixed strategy Nash equilibrium occurs when no player can improve their outcome by changing their strategy, given the probabilities of the other player's strategies.
Draw the probability tree diagram for flipping the coin two times showing the outcome?
Each toss outcome has a probability of 1/2; picture copied from the related link. The related link does a good job explaining tree diagrams and probabilities.
What is the sequence of 107 214 642 2568 12840?
Each number is multiplied by an incrementing value. 107 is multiplied by 2, 214 is multiplied by 3, 642 is multiplied by 4 and so on.
How do you give the probability of a sum?
You find the event space for the random variable that is the required sum and then calculate the probabilities of each favourable outcome. In the simplest case it is a convolution of the probability distribution functions.
If the standard deviation of the final was 12 points and if each value in the data set where multiplied by 1.75 what would be the standard deviation of the resulting data?
If each value in a data set is multiplied by a constant, the standard deviation of the resulting data set is also multiplied by that constant. In this case, since the original standard deviation is 12 points and each value is multiplied by 1.75, the new standard deviation would be 12 * 1.75 = 21 points.
Definition of product in math terms?
The definition of a product is the outcome number of two or more numbers that have been multiplied by each other.
What re the three criteria needed for something to be a probability distribution?
A probability distribution must have a well defined domain - that is, the set of possible outcomes.For each possible outcome, there must be a non-negative value associated - the probability of that outcome.The sum of the probabilities, over all possible outcomes, must be 1.
How do you calculate expected rate of return?
The expected rate of return is calculated by multiplying the potential returns of each possible outcome by their probabilities and then summing these values. The formula is: Expected Rate of Return = (Probability of Outcome 1 × Return of Outcome 1) + (Probability of Outcome 2 × Return of Outcome 2) + ... + (Probability of Outcome n × Return of Outcome n). This approach helps investors assess the average return they might anticipate from an investment based on various scenarios.
