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In some situationsX is continuous but Y is discrete. For example, in a logistic regression, one may wish to predict the probability of a binary outcome Y conditional on the value of a continuously-distributed X. In this case, (X, Y) has neither a probability density function nor a probability mass function in the sense of the terms given above. On the other hand, a "mixed joint density" can be defined in either of two ways:
Formally, fX,Y(x, y) is the probability density function of (X, Y) with respect to the product measure on the respective supports of X and Y. Either of these two decompositions can then be used to recover the joint cumulative distribution function:
The definition generalizes to a mixture of arbitrary numbers of discrete and continuous random variables.
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What is the likelihood of the probability 0 to infinity?
The answer depends on the probability distribution function for the random variable.
What does the mean have to do with a normal distribution?
Almost all statistical distribution have a mean. It is the expected value of the random variable which is distributed according to that function.
Define a normal random variable?
I have included two links. A normal random variable is a random variable whose associated probability distribution is the normal probability distribution. By definition, a random variable has to have an associated distribution. The normal distribution (probability density function) is defined by a mathematical formula with a mean and standard deviation as parameters. The normal distribution is ofter called a bell-shaped curve, because of its symmetrical shape. It is not the only symmetrical distribution. The two links should provide more information beyond this simple definition.
Can the Poisson distribution be a continuous random variable or a discrete random variable?
True
How often the value of a random variable is at or below a certain value.?
The probability of a random variable being at or below a certain value is defined as the cumulative distribution function (CDF) of the variable. The CDF gives the probability that the variable takes on a value less than or equal to a given value.
How do you get the median of a continuous random variable?
You integrate the probability distribution function to get the cumulative distribution function (cdf). Then find the value of the random variable for which cdf = 0.5.
What gives the probability of each random variable?
The marginal probability distribution function.
What is the likelihood of the probability 0 to infinity?
The answer depends on the probability distribution function for the random variable.
How many random variables are needed to plot a probability distribution?
A probability density function can be plotted for a single random variable.
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 are the 2 conditions that determine a probability distribution?
The value of the distribution for any value of the random variable must be in the range [0, 1]. The sum (or integral) of the probability distribution function over all possible values of the random variable must be 1.
What does the mean have to do with a normal distribution?
Almost all statistical distribution have a mean. It is the expected value of the random variable which is distributed according to that function.
Can the Poisson distribution be a continuous random variable or a discrete random variable?
True
Define a normal random variable?
I have included two links. A normal random variable is a random variable whose associated probability distribution is the normal probability distribution. By definition, a random variable has to have an associated distribution. The normal distribution (probability density function) is defined by a mathematical formula with a mean and standard deviation as parameters. The normal distribution is ofter called a bell-shaped curve, because of its symmetrical shape. It is not the only symmetrical distribution. The two links should provide more information beyond this simple definition.
What is the probability the random variable will assume a value between 40 and 60?
It depends on what the random variable is, what its domain is, what its probability distribution function is. The probability that a randomly selected random variable has a value between 40 and 60 is probably quite close to zero.
What is discrete probability distribution?
It is a function that gives the probabilities associated with the discrete number of values that a random variable can take.
What is Cauchy?
Cauchy distribution is the distribution of a random variable along a specific function. In AI, this distribution is used to generate adaptive models which produce fast learning across dimensions.
