Answered: Find fQ|X (q|x) for x ∈ {0, 1} and all q.

A First Course in Probability (10th Edition)

10th Edition

ISBN: 9780134753119

Author: Sheldon Ross

Publisher: PEARSON

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Question

Let Q be a continuous random variable with PDF
f_Q(q)= 6q(1 − q) if 0 ≤ q ≤ 1
f_Q(q) = 0 otherwise
This Q represents the probability of success of a Bernoulli random variable X, i.e.,
P (X = 1 | Q = q) = q.
Find f_Q|X (q|x) for x ∈ {0, 1} and all q.

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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