Mathematics: Evaluate the cumulative distribution function, f, for the given random variable, x, at specified values: also determine the requested probabilities. f(x) = (125/31) (1/5)^x, x = 1, 2, 3 give exact answers in form of fraction. f(1) = (2) = (3) = (a) p(x lessthanorequalto 1.5) =) p(x lessthanorequalto 3) =) p(x 2) =) p(1 x lessthanorequalto 2) =

it took me a while but the answer is 5/3...

Evaluate the cumulative distribution function, f,

evy22

11.01.2022

Step-by-step explanation:

Given that x is a random variable with probability density function given as

$f(x) =\frac{125}{31} *\(frac{1}{5} )^x, x=1,2,3$

To find cumulative function for x

F(1) = $f(1) = \frac{125}{31*5} =\frac{25}{31}$

F(2) = $f(1)+f(2)\\=\frac{25}{31} +\frac{125}{31}*\frac{1}{25}=\frac{30}{31}$

F(3) = $f(1)+f(2)+f(3)\\= \frac{30}{31}+\frac{125}{31*125}\\=1$

a) P(X lessthanorequalto 1.5)

= $P(X\leq 1.5) = F(1)\\=\frac{25}{31}$

(b) P(X lessthanorequalto 3) =__F(3) = 1_________

(d) P(1 < X lessthanorequalto 2) =__f(2) = 25/31____

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