Answer :
Answer:
Step-by-step explanation:
Given that x is a random variable with probability density function given as
[tex]f(x) =\frac{125}{31} *\(frac{1}{5} )^x, x=1,2,3[/tex]
To find cumulative function for x
F(1) = [tex]f(1) = \frac{125}{31*5} =\frac{25}{31}[/tex]
F(2) = [tex]f(1)+f(2)\\=\frac{25}{31} +\frac{125}{31}*\frac{1}{25}=\frac{30}{31}[/tex]
F(3) = [tex]f(1)+f(2)+f(3)\\= \frac{30}{31}+\frac{125}{31*125}\\=1[/tex]
a) P(X lessthanorequalto 1.5)
=[tex]P(X\leq 1.5) = F(1)\\=\frac{25}{31}[/tex]
(b) P(X lessthanorequalto 3) =__F(3) = 1_________
(c) P(X > 2) =__f(3) = 1/31________
(d) P(1 < X lessthanorequalto 2) =__f(2) = 25/31____