Question

The sample space of a random experiment is {a, b, c, d, e, f}, and each outcome is equally likely. A random variable is defined as follows:
Outcome a b c d e f
X 0 0 1.4 1.4 2 3
Determine the probability mass function of X. Use the probability mass function to determine the following probabilities.
A) P(X = 1.6).B) P(0.5 < X < 2.7).C) P(X > 3).D) P(0 ≤ X < 2).E) P(X = 0 or X = 2).

Answer 1

Answer:

X ____ : 0 ______ 1.4 _____ 2 _____ 3

P(X) ___ 1/3 _____ 1/3 _____ 1/6 ____ 1/6 ;

0 ;

1/2 ;

0 ;

2/3 ;

1/2

Step-by-step explanation:

Each has the same probability ;

X ___ : 0 ___ 0 ___ 1.4 ____1.4 ___ 2 ___ 3

P(x) __ 1/6 __1/6 ___ 1/6 ___ 1/6 ___1/6 __ 1/6

Probability : required outcome / Total possible outcomes

X = 0

P(x = 0) = 1/6 + 1/6 = 2/6 = 1/3

X = 1.4

P(x = 1.4) = 1/6 + 1/6 = 2/6 = 1/3

X = 2

P(X) = 1/6

X = 3

P(x) = 1/6

Hence ;

X ____ : 0 ______ 1.4 _____ 2 _____ 3

P(X) ___ 1/3 _____ 1/3 _____ 1/6 ____ 1/6

A) P(X = 1.6).B) P(0.5 < X < 2.7).C) P(X > 3).D) P(0 ≤ X < 2).E) P(X = 0 or X = 2).

A.)

P(X = 1.6) = 0

B.)

P(0.5 < X < 2.7) = p(x = 1.4) + p(x = 2)

P(0.5 < X < 2.7) = 1/3 + 1/6 = (2 + 1) / 6 = 3/6 = 1/2

C.)

P(X > 3) = 0

D.)

P(0 ≤ X < 2) = P(0) + P(1.4)

P(0) + P(1.4) = 1/3 + 1/3 = 2/3

E.)

P(X = 0 or X = 2) = 1/3 + 1/6 = (2 + 1)/6 = 3/6 = 1/2