Final answer:
The random variable W = 1 - Y, where Y follows a Beta(2,4) distribution, will have a Beta(4,2) distribution. This is because the transformation flips the Beta distribution, exchanging the roles of its parameters.
Step-by-step explanation:
If a random variable Y follows a Beta(2,4) distribution, then the random variable W = 1 - Y will follow a Beta distribution that reflects the transformation. To find the parameters of the Beta distribution that W follows, consider the properties of the Beta distribution. The Beta distribution is defined on the interval [0, 1], and the transformation W = 1 - Y essentially flips the distribution, exchanging the roles of successes and failures for the original variable Y.
The correct answer to what distribution W follows is E) W follows a Beta(4,2) distribution. This is because if Y has parameters (a, b), the transformed variable 1 - Y will have parameters (b, a), as it represents the distribution of 'failures' rather than 'successes' when interpreting the Beta distribution in the context of successes (first parameter) and failures (second parameter).