Conditional Probability Homework Help

Twitter

Get Professional Statistics Assignment Help in Conditional Probability from Tutorchrome statistics assignment experts. offering 24x7 Statistics Assignment Writing Help to university students across the USA, Canada, UK, Australia and UAE countries.

 CONDITIONAL PROBABILITY

Conditional probability can be defined as the probability that an event will occur when another event is known to occur or to have occurred and if the events are A and B respectively, then it is represented as "the probability of A given B" which is represented as P(A|B).  it is also represented as P_B(A) where P(A|B) may or may not be equal to the probability of A that is P(A). If they are equal then A and B are independent and an example is if a coin is flipped two times then the outcome of the second flip is independent of the outcome of the first.

In the Bayesian probability, the conditioning event is interpreted as evidence for the conditioned event that is P(A) is the probability of A before accounting for evidence E, and P(A|E) is the probability of A having accounted for evidence E.

Conditioning on an event

According to Kolmogorov definition, given two events A and B with P(B) > 0, then the conditional probability is defined as the quotient of the joint probability of A and B, and the probability of B  and it is represented as follows

Some authors, such as Bruno de Finetti prefer to introduce conditional probability as a Probability axioms  and it is represented as follows

Although mathematically equivalent, this may be preferred philosophically that under major probability interpretations such as the subjective probability as well as the conditional probability is considered as a primitive entity and further, this "multiplication axiom" introduces a symmetry with the summation axiom for mutually exclusive events and it will be represented as follows

Conditional Probability Assignment Help

Conditioning on a random variable

Conditioning on an event may be generalized to conditioning on a random variable where X be a random variable taking some value from x_n. Let A be an event, then the conditional probability of A given X is defined as the random variable and it is represented as follows

More formally it is represented as follows

The conditional probability P(A|X) is a function of X that is the function g is defined as follows

,

then

Note that P(A|X) and X are now both random variables and from the Law of total probability the expected value of P(A|X) is equal to the unconditional probability of A.