Final answer:
The cumulative distribution function (CDF) of Y = 3X, where X is exponential with a mean of 1/3, is 1 - e^(-0.5y/3).
Step-by-step explanation:
To find the CDF of Y = 3X, where X is exponential with a mean of 1/3, we need to use the properties of the exponential distribution. Since X ~ Exp(0.5), the cumulative distribution function (CDF) of X is given by P(X < x) = 1 - e^(-0.5x).
Substituting Y = 3X, we have P(Y < y) = P(3X < y) = P(X < y/3) = 1 - e^(-0.5y/3).
Therefore, the CDF of Y = 3X is 1 - e^(-0.5y/3).