SURIGAO STATE COLLEGE
OF TECHNOLOGY
CLAVER EXTENSION COLLEGE
P-7 Tayaga, Claver, Surigao del Norte
Name: John Wayne Atig
Course: BS in Civil Engineering
Date: March 10, 2021
Subject:
Pre – Test Module 3
Discreet Random Variables and Probability Distributions
Direction: Read the problems carefully. Write your solutions in a separate sheet of paper.
1. A fair coin is flipped 3 times. Consider a random variable 𝑋, which is the number of runs. The number of runs is number of
changes of letter H and T. For example, HHH has one run, TTH has two runs, and THT has three runs. Find the probability
distribution of the random variable 𝑋.
2. A fair coin is flipped four times. Let 𝐻 denote a head is obtained and 𝑇 denote a tail is obtained in a flip.
a. Find the probability that the outcome is 𝐻𝐻𝑇𝐻 in that order.
b. Find the probability that exactly 3 heads are obtained in 4 flips.
3. Let 𝑋 have probability distribution
a. Find the cumulative distribution function 𝐹(𝑥) of 𝑋.
b. Find the probability that 𝑋 is odd.
c. Find 𝐸(𝑋).
d. Find 𝑉𝑎𝑟(𝑋).
4. Eighteen individuals are scheduled to take a driving test at a particular DMV office on a certain day, eight of whom will be
taking the test for the first time. Suppose that six of these individuals are randomly assigned to a particular examiner, and let
𝑋 be the number among the six who are taking the test for the first time.
a. What kind of a distribution does 𝑋 have (name and values of all parameters)?
b. Compute 𝑃 (𝑋 = 2), 𝑃 (𝑋 ≤ 2), and 𝑃 (𝑋 ≥ 2).
c. Calculate the mean value and standard deviation of 𝑋.
5. An article in the Los Angeles Times (Dec. 3, 1993) reports that 1 in 200 people carry the defective gene that causes inherited
colon cancer. In a sample of 1000 individuals, what is the approximate distribution of the number who carries this gene? Use
this distribution to calculate the approximate probability that
a. Between 5 and 8 (inclusive) carry the gene.
b. At least 8 carry the gene.