ENGR371 PROBABILITY AND STATISTICS SECTION W CONCORDIA UNIVERSITY

ENGR371 PROBABILITY AND STATISTICS SECTION W
CONCORDIA UNIVERSITY



Concordia University
ENGR371 – Probability and Statistics
Section W

Midterm Exam II Winter

1) (5 Marks) Let f (x)  kx 2 , if 0 ≤ x ≤ 2 and 0 otherwise be the pdf of a random
variable X.
a) Find the value of k.
b) Find c such that P(X ≤ c) = 0.1.
c) Find the CDF of X.

2) (5 Marks) Flaws occur in the interior of plastic used for automobiles according to a
Poisson distribution with a mean of 0.02 flaw per panel
a) If one panel is inspected, what is the probability that there are no flaws?
b) If 50 panels are inspected, what is the probability that there are no flaws?
c) What is the expected number of panels that need to be inspected before a flaw is
found?

3) (5 Marks) The line width for semiconductor manufacturing is assumed to be
normally distributed with a mean of 0.5mm and a standard deviation of 0.05mm.
a) What is the probability that a line width is greater than 0.62mm?
b) What is the probability that a line width is between 0.47 and 0.63 mm?
c) The line width of 90% of samples is below what value?

4) (5 Marks) The life time in years of a certain type of electrical switch has an
exponential distribution with an average life of   2 .
a) What is the probability that a switch fails in the first year?
b) If 100 of these switches are installed in different systems, let random
variable X be the number of switches that fail during the first year. What is the
probability distribution function f (x) of X ?
c) What is approximately the probability that at most 30 out of the 100 switches fail
during the first year?