Question

The sample space of a random experiment is fa, b, c, d, e, fI , and each outcome is equally likely. A random variable is defined as follows outcome abcde 0 03.9 7 715 Evaluate the cumulative distribution function of X at specified values. [Give exact answers in form of fraction.] F(0) F(3.9) F(7) F (15)

Answer 1

Given data,

Outcomes	a	b	c	d	e	f
X	0	0	3.9	7	7	15
probability	1/6	1/6	1/6	1/6	1/6	1/6

The cumulative distribution function of a real-valued random variable ${\displaystyle X}$ is the function given by

${\displaystyle F_{X}(x)=\operatorname {P} (X\leq x)}$

Therefore from given data we calculate

$1) F(0) = P(X\leq 0) = P(X=0) = 1/6$

$2) F(3.9) = P(X\leq 3.9) = P(X=0)+ P(X=3.9) = 2/6+1/6 =3/6$

$3) F(7) = P(X\leq 7) = P(X=0)+ P(X=3.9)+P(X=7) = 2/6+1/6 +2/6 =5/6$

$4) F(15) = P(X\leq 15) = P(X=0)+ P(X=3.9)+P(X=7) +P(X=15)= 2/6+1/6 +2/6 +1/6 = 6/6$

Therefore

x	0	3.9	7	15
p(x)	2/6	1/6	2/6	1/6
F(X)	2/6	3/6	5/6	6/6