Let X be a continuous random variable whose cumulative distribution function (CDF) F_X(x), for some t, is given as follo...

Question

Let X be a continuous random variable whose cumulative distribution function (CDF) F_X(x), for some t, is given as follows:

F_X(x) = 0            for x < t
             (x - t)/(4 - t)   for t <= x <= 4
             1            for x > 4

If the median of X is 3, then what is the value of t?

A. 2
B. 1
C. -1
D. 0

Accepted Answer

t = 2. Answer A. The CDF linearly rises from 0 at x=t to 1 at x=4, meaning X is uniformly distributed on [t, 4]. The median is the value m where F_X(m)=0.5. Setting F_X(3)=0.5 gives (3-t)/(4-t) = 0.5, which is a linear equation in t with solution t=2.

Let X be a continuous random variable whose cumulative distribution function (CDF) F_X(x), for some t, is given as follows: F_X(x) = 0 for x < t (x - t)/(4 - t) for t <= x <= 4 1 for x > 4 If the median of X is 3, then what is the value of t? A. 2 B. 1 C. -1 D. 0