General Electric models the time X in years that a new microwave will last using the following PDF f(x)= (3x2e(−x^3/8^3))/8^3, x>0 (a)  Write out the CDF and quantile formulas. (b)  What proportion of microwaves does GE anticipate will last at least 10 years? (c)  What is the median length of time until failure for a new microwave?

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.