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Probability density functions: Discrete random variables.

3. Aminah decides to replace the two used batteries in her torch with new ones. Unfortunately, when she takes them out, she mixes them up with three new batteries. All five batteries are identical in appearance. Aminah selects two of the batteries at random. Draw up a probability distribution table for X, the number of new batteries that Aminah selects. 4. The discrete random variable X has the probability function kx x = 2,4.6 P(X = x) = k(x - 2) x =8 0 otherwise Where k is a constant. a) Show that k =1/18 b) Find the exact value of F(5). a) Find the exact value of E(X) b) Find the exact value of E(X2) c) Calculate Var (3-4X) giving your answer to 3 d.p