Question

Suppose that the lifetime of a battery (in thousands of hours) is a random variable X...

Suppose that the lifetime of a battery (in thousands of hours) 
is a random variable X whose p.d.f. is given by: 

         { 0            x <= 0
 f(x) =  {
         { ke^(-2x)     0 < x


(a) Find the constant k to make this a legitimate p.d.f. 
        Also sketch this p.d.f. [Hint: improper integral.] 

(b) Determine the c.d.f. of X. Also sketch this c.d.f.

(c) Determine the mean [Hint: Integration By Parts] ...
        ... and median of X, and comment on how they compare.

(d) Determine the probability that ...
        ... the battery lasts longer than its mean lifetime.

(e) If the manufacturer only wants to replace 7% of the batteries
    under warranty, where should the manufacturer set the warranty?
Math   Statistics-And-Probability   
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