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What is the total probability of discrete random variable?
A discrete random variable has a countable number of possible values. The probability of each value of a discrete random variable is between 0 and 1, and the sum of all the probabilities is equal to 1. A continuous random variable takes on all the values in some interval of numbers.
Is probability continuous or discrete?
For a discrete distribution, probabilities can be assigned to the values in the distribution – for example, “the probability that the web page will have 12 clicks in an hour is 0.15.” In contrast, a continuous distribution has an infinite number of possible values, and the probability associated with any particular …
How is conditional probability different from discrete probability?
The ideas behind conditional probability for continuous random variables are very similar to the discrete case. The difference lies in the fact that we need to work with probability density in the case of continuous random variables.
How is the law of total probability extended?
The law of total probability extends to the case of conditioning on events generated by continuous random variables. Let be a probability space. Suppose . Then the law of total probability states P ( A ) = ∫ − ∞ ∞ P ( A | X = x ) d F X ( x ) . {displaystyle P (A)=int _ {-infty }^ {infty }P (A|X=x)dF_ {X} (x).}
Which is an example of a conditional PDF?
As another example, if you have two random variables X and Y, you can write P(X ∈ C | Y ∈ D) = P(X ∈ C, Y ∈ D) P(Y ∈ D), where C, D ⊂ R. However, sometimes we need to use the concepts of conditional PDFs and CDFs. The formulas for conditional PDFs and CDFs of continuous random variables are very similar to those of discrete random variables.
How is the conditional expectation and variance defined?
The conditional expectation and variance are defined by replacing the PDF by conditional PDF in the definitions of expectation and variance. In general, for a random variable X and an event A, we have the following: Let X ∼ Exponential(1) . Find the conditional PDF and CDF of X given X > 1. Find E[X | X > 1].