PROBABILITY AND STATISTICS IN COMPUTER SCIENCE AND
SOFTWARE ENGINEERING - MIDTERM 2 REVIEW 2026
hw:5 q:1
The lifetime, in years, of some electronic component is a continuous random variable with
the density
f(x) = k/x^4 for x >= 1
f(x) = 0 for x < 1
Find k, the cumulative distribution function, and the probability for the lifetime to exceed 2
years. -ANSWER-
hw:5 q:2
The time, in minutes, it takes to reboot a certain system is a continuous variable with the
density
f(x) = C(10-x)^2 if 0<x<100
f(x) = 0 otherwise
(a) Compute C.
(b) Compute the probability that it takes between 1 and 2 minutes to reboot. -ANSWER-
hw:5 q:3
A program is divided into 3 blocks that are being compiled on 3 parallel computers. Each
block takes an Exponential amount of time, 5 minutes on the average, independently of
other blocks. The program is completed when all the blocks are compiled. Compute the
expected time it takes the program to be compiled. -ANSWER-
, hw:5 q:4
The time it takes a printer to print a job is an Exponential random variable with the
expectation of 12 seconds. You send a job to the printer at 10:00 am, and it appears to be
third in line. What is the probability that your job will be ready before 10:01? -ANSWER-
hw:5 q:5
For some electronic component, the time until failure has Gamma distribution with
parameters α = 2 and λ = 2 (years−1). Compute the probability that the component fails
within the first 6 months. -ANSWER-
hw:5 q:6
Consider a satellite whose work is based on a certain block A. This block has an independent
backup B. The satellite performs its task until both A and B fail. The lifetimes of A and B are
exponentially distributed with the mean lifetime of 10 years.
(a) What is the probability that the satellite will work for more than 10 years?
(b) Compute the expected lifetime of the satellite. -ANSWER-
hw:5 q:7
A computer processes tasks in the order they are received. Each task takes an Exponential
amount of time with the average of 2 minutes. Compute the probability that a package of 5
tasks is processed in less than 8 minutes. -ANSWER-
hw:6 q:1
Let Z be a Standard Normal random variable. Compute
(d) P(|Z| ≤ 1.25)
(g) With probability 0.8, variable Z does not exceed what value? -ANSWER-
hw:6 q:2
For a Normal random variable X with E(X) = −3 and Var(X) = 4, compute
(d) P(|X + 3| ≥ 2.39)
SOFTWARE ENGINEERING - MIDTERM 2 REVIEW 2026
hw:5 q:1
The lifetime, in years, of some electronic component is a continuous random variable with
the density
f(x) = k/x^4 for x >= 1
f(x) = 0 for x < 1
Find k, the cumulative distribution function, and the probability for the lifetime to exceed 2
years. -ANSWER-
hw:5 q:2
The time, in minutes, it takes to reboot a certain system is a continuous variable with the
density
f(x) = C(10-x)^2 if 0<x<100
f(x) = 0 otherwise
(a) Compute C.
(b) Compute the probability that it takes between 1 and 2 minutes to reboot. -ANSWER-
hw:5 q:3
A program is divided into 3 blocks that are being compiled on 3 parallel computers. Each
block takes an Exponential amount of time, 5 minutes on the average, independently of
other blocks. The program is completed when all the blocks are compiled. Compute the
expected time it takes the program to be compiled. -ANSWER-
, hw:5 q:4
The time it takes a printer to print a job is an Exponential random variable with the
expectation of 12 seconds. You send a job to the printer at 10:00 am, and it appears to be
third in line. What is the probability that your job will be ready before 10:01? -ANSWER-
hw:5 q:5
For some electronic component, the time until failure has Gamma distribution with
parameters α = 2 and λ = 2 (years−1). Compute the probability that the component fails
within the first 6 months. -ANSWER-
hw:5 q:6
Consider a satellite whose work is based on a certain block A. This block has an independent
backup B. The satellite performs its task until both A and B fail. The lifetimes of A and B are
exponentially distributed with the mean lifetime of 10 years.
(a) What is the probability that the satellite will work for more than 10 years?
(b) Compute the expected lifetime of the satellite. -ANSWER-
hw:5 q:7
A computer processes tasks in the order they are received. Each task takes an Exponential
amount of time with the average of 2 minutes. Compute the probability that a package of 5
tasks is processed in less than 8 minutes. -ANSWER-
hw:6 q:1
Let Z be a Standard Normal random variable. Compute
(d) P(|Z| ≤ 1.25)
(g) With probability 0.8, variable Z does not exceed what value? -ANSWER-
hw:6 q:2
For a Normal random variable X with E(X) = −3 and Var(X) = 4, compute
(d) P(|X + 3| ≥ 2.39)
