Question

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) = ____________F(2) = __________F(3) =____________ (a) P(X lessthanorequalto 1.5) =____________(b) P(X lessthanorequalto 3) =___________(c) P(X > 2) =__________(d) P(1 < X lessthanorequalto 2) =______

Answer 1

Answer:

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_________

(c) P(X > 2) =__f(3) = 1/31________

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