0
Add your answer:
Earn +20 pts
Difference between a random variable and a probability distribution is?
A random variable is a variable that can take different values according to a process, at least part of which is random.For a discrete random variable (RV), a probability distribution is a function that assigns, to each value of the RV, the probability that the RV takes that value.The probability of a continuous RV taking any specificvalue is always 0 and the distribution is a density function such that the probability of the RV taking a value between x and y is the area under the distribution function between x and y.
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.
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 is a uniform probability distribution?
It is a probability distribution where when all of the values of a random variable occur with equal probability. Say X is the random variable, such as what number shows up when we roll a die. There are 6 possible outcomes, each with a 1/6 probability of showing up. If we create a probability distribution where X= 1,2,3,4,5, or 6, we note P(X=k)=1/k where k is any number between 1 and 6 in this case. The graph will be a rectangle.
If an event has a 1 in 4 chance of occurring what is the probability of it happening to one individual in a sample of five?
If we assume that the probability of an event occurring is 1 in 4 and that the event occurs to each individual independently, then the probability of the event occurring to one individual is 0.3955. In order to find this probability, we can make a random variable X which follows a Binomial distribution with 5 trials and probability of success 0.25. This makes sense because each trial is independent, the probability of success stays constant for each trial, and there are only two outcomes for each trial. Now you can find the probability by plugging into the probability mass function of the binomial distribution.
Difference between a random variable and a probability distribution is?
A random variable is a variable that can take different values according to a process, at least part of which is random.For a discrete random variable (RV), a probability distribution is a function that assigns, to each value of the RV, the probability that the RV takes that value.The probability of a continuous RV taking any specificvalue is always 0 and the distribution is a density function such that the probability of the RV taking a value between x and y is the area under the distribution function between x and y.
What is the difference between probability distribution and probability density function?
A probability density function assigns a probability value for each point in the domain of the random variable. The probability distribution assigns the same probability to subsets of that domain.
Explain probability distribution?
A probability distribution describes the likelihood of different outcomes in a random experiment. It shows the possible values of a random variable along with the probability of each value occurring. Different probability distributions (such as uniform, normal, and binomial) are used to model various types of random events.
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.
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 is a uniform probability distribution?
It is a probability distribution where when all of the values of a random variable occur with equal probability. Say X is the random variable, such as what number shows up when we roll a die. There are 6 possible outcomes, each with a 1/6 probability of showing up. If we create a probability distribution where X= 1,2,3,4,5, or 6, we note P(X=k)=1/k where k is any number between 1 and 6 in this case. The graph will be a rectangle.
What is uniform distribution?
It is a probability distribution where when all of the values of a random variable occur with equal probability. Say X is the random variable, such as what number shows up when we roll a die. There are 6 possible outcomes, each with a 1/6 probability of showing up. If we create a probability distribution where X= 1,2,3,4,5, or 6, we note P(X=k)=1/k where k is any number between 1 and 6 in this case. The graph will be a rectangle.
What is a uniform distribution?
It is a probability distribution where when all of the values of a random variable occur with equal probability. Say X is the random variable, such as what number shows up when we roll a die. There are 6 possible outcomes, each with a 1/6 probability of showing up. If we create a probability distribution where X= 1,2,3,4,5, or 6, we note P(X=k)=1/k where k is any number between 1 and 6 in this case. The graph will be a rectangle.
Is the mean of probability distribution is called its expected value?
No. The mean is the expected value of the random variable but you can also have expected values of functions of the random variable. If you define X as the random variable representing the result of a single throw of a fair die, the expected value of X is 3.5, the mean of the probability distribution of X. However, you play a game where you pay someone a certain amount of money for each throw of the die and the other person pays you your "winnings" which depend on the outcome of the throw. The variable, "your winnings", will also have an expected value. As will your opponent's winnings.
If an event has a 1 in 4 chance of occurring what is the probability of it happening to one individual in a sample of five?
If we assume that the probability of an event occurring is 1 in 4 and that the event occurs to each individual independently, then the probability of the event occurring to one individual is 0.3955. In order to find this probability, we can make a random variable X which follows a Binomial distribution with 5 trials and probability of success 0.25. This makes sense because each trial is independent, the probability of success stays constant for each trial, and there are only two outcomes for each trial. Now you can find the probability by plugging into the probability mass function of the binomial distribution.
How do you compute expected value from random discreet variable?
Follow these steps:Find all the values that the random variable (RV) can take, x.For each x, find the probability that the RV takes than value, p(x).Multiply them: x*p(x).Sum these over all possible values of x.The above sum is the expected value of the RV, X.
What is the formula of a mean?
Obtain the arithmetic mean of a batch of numbers by adding them up and dividing by their count. For example, the arithmetic mean of 3, 5, and 10 equals (3 + 5 + 10)/ 3 = 6. There are other kinds of means, such as geometric and harmonic, but usually when the type of mean is not specified the arithmetic mean is intended. For completeness I will also provide an answer from probability theory. The mean of a random variable is its expectation, which is defined to be its integral. If the random variable has a distribution f(x)dx, its mean equals the integral of x*f(x)dx over all real numbers. This is related to the first definition of arithmetic mean. A batch of numbers gives rise to a random variable supported at those numbers, where the probability of each number is proportional to the number of times it occurs in the batch. (This is the empirical distribution function of the batch.) The arithmetic mean of the batch equals the expectation of that random variable.
