Zero.
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.
It is a discrete random variable.
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.
For a discrete variable, you add together the probabilities of all values of the random variable less than or equal to the specified number. For a continuous variable it the integral of the probability distribution function up to the specified value. Often these values may be calculated or tabulated as cumulative probability distributions.
No.
No. The probability that a continuous random variable takes a specific value is always zero.
Yes. It is a continuous variable. As used in probability theory, it is an example of a continuous random variable.
Yes.
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.
It is a discrete random variable.
In probability theory, the expectation of a discrete random variable X is the sum, calculated over all values that X can take, of : the product of those values and the probability that X takes that value. In the case of a continuous random variable, it is the corresponding integral.
True
The formula, if any, depends on the probability distribution function for the variable. In the case of a discrete variable, X, this defines the probability that X = x. For a continuous variable, the probability density function is a continuous function, f(x), such that Pr(a < X < b) is the area under the function f, between a and b (or the definite integral or f, with respect to x, between a and b.
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.
The integral of the density function from the given point upwards.
I am not quite sure what you are asking. If this answer is not complete, please be more specific. There are many probability density functions (pdf) of continuous variables, including the Normal, exponential, gamma, beta, log normal and Pareto. There are many links on the internet. I felt that the related link gives a very "common sense" approach to understanding pdf's and their relationship to probability of events. As explained in the video, a probability can be read directly from a discrete distribution (called a probability mass function) but in the case of a continuous variable, it is the area under the curve that represents probability.
A discrete random variable (RV) can only take a selected number of values whereas a continuous rv can take infinitely many.