Question

Suppose that a random variable X has a DISCRETE distribution with probability mass function given as: P(x) = ( x / 2485 if x = 1, 2, . . . , 70 0 Otherwise a) Find P(x > 5) b) Find P(2 ≤ x ≤ 68) c) Find P(x = 70.5)

Answer 1

Solution.

$Р(x)=\begin{Bmatrix} \frac{x}{2485}, \text{if }x=1,2,...,70 \\ 0, otherwise \end{Bmatrix}$

a)

$P(x>5)=1-P(x\leq 5)=1-\frac{1}{2485}-\frac{2}{2485}-\frac{3}{2485}-\frac{4}{2485}-\frac{5}{2485}=1-\frac{15}{2485}=\frac{2470}{2485}=0.994$

b)

$P(2\leq x\leq 68)=P(68)-P(2)=\frac{68}{2485}-\frac{2}{2485}=\frac{66}{2485}=0.027$

c)

70.5>70, so 70.5 in otherwise.

$P(x=70.5)=0$