A random variable X is uniformly distributed in the interval (-л/2, π/2). Xis transformed to a new random variable Y= T(x) = a tan(x), where a > 0. Find the probability density function of Y.

Let X be a uniform random variable on the interval (-3,3) and let Y = X^2 A) find E(Y). B) find the probability density function of Y

Let  X be a continuous random variable with range  [−ln5,0]  and its probability density function is given by the following function: f(x)=ce^−x, where  cc is a constant.  (1) Find the value of  c . Answer:   (2) Find the probability  P(−ln2≤X≤0) . Answer:

A machine has a useful life of 4 to 9 years, and its life (in years) has a probability density function defined by f(x) = 1 1 Find the probability that the useful life of such a machine selected 15 at random will be longer than 7 years?

The diameter of a particle of contamination (in micrometers) is modeled with the probability density function 2 f(x)= = x3 for x > 1 . What is the probability that the diameter of the particle of contamination is below 2 micrometers?