Given the following function: it: 0 0 0 1:30 Find the probabilities that one of these lightbulbs will provide satisfactory illumination for 0 at most

Given the following function: it: 0<:r: f elsewhere find the corresponding distribution function and verify that this is a legitimate probability density determine random variable having distri- bution will take on value greater than between length of satisfactory illumination in years provided by certain model lightbulb i ie zr>0 0 1:30 Find the probabilities that one of these lightbulbs will provide satisfactory illumination for 0 at most 2.5 years 0 between 4 and 6 years 0 at least 6.75 years For the following probability density, nd the mean and variance: f(:r)={%(13'2) 053351 0 elsewhere The time for an epoxy to cure can be treated as a random variable having a normal distribution with a mean of 30 seconds. Find the standard deviation if the probability is 0.2 that it will take on a value greater than 39.2 seconds I am designing a ow reactor and need glass tubes with an inside diameter of 0.300 :I: 0.005 inch. The tubes may be considered a random variable having a normal distri- bution with it = 0.302 inch and o = 0.003 inch. What percentage of these tubes will meet my specications? Show that the following two equations for 0'2 are equivalent: [:(sc mews: /: :32f[:r)d:r p2