Let X be a discrete random variable with probability mass function given in the following table: O 30 60 90 p(x) | 0.3 0.2 0.4 0.1 Find the following probabilities: (i) P(45 < X < 90) = (ii) P(X > 15) : (iii) P(X < 30) =

Suppose that a discrete random variable X has a distribution with the following probability (4cx,x = 2,3,5 ( 0, otherwise function: f(x) a. Determine the value of the constant c: b. Calculate Pr (X > 3) (please use the value of c from part a.):

A random variable X has a following probability function, X 0 1 3 4 5 6 P(X) 0k 2k 2k | 3k k 2k 7k2 + k Find the value of, (i) k (ii) P(X < 6).

The probability function of the amount of soft drink in a can is f(x)=4cx for11.5 <X< 12.5 oz. Determine the value of c such that f(x) represents a p.d.f..Then, find the following probabilities:(a) P(X > 11.5), (b) P(X < 12.25), and (c) P(11.75 <X< 12.25).