Kingdom of Saudi Arabia
Ministry of High Education
Majmaah University
Faculty of sciences in AlZulfi
A
1433/6/18 ‫التاريخ‬
‫الزمن ساعة‬
‫بسم هللا الرحمن الرحيم‬
‫المستوي الثالث‬
‫المملكة العربية السعودية‬
‫وزارة التعليم العالي‬
‫جامعة المجمعة‬
‫كلية العلوم بالزلفي‬
)STA 202( ‫ نظرية التوزيعات االحتمالية‬: ‫المادة‬
:‫الرقم الجامعي‬
: ‫اسم الطالب‬
1. The random variable N has the probability Mass Function
c / n n  1,2,3
PN (n)  
 0 otherwise
a. Find the value of the constant C.
b. find P[ N  1]
c. Find P[ N  2]
d. Find P[ N  3]
2. Suppose you test one circuit. With probability P the circuit is rejected let X
be the number of rejected circuits in one test. What is the probability Mass
function PX (x) ?
3. The random variable R has the probability Mass Function
r 0
1 / 4

PR (r )  3 / 4
r 1
 0 otherwise

a. Find and sketch the CDF of random variable R?
b. What is E (R ) , Var (R ) , and  R ?
4. If Y  aX  b prove that
E (Y )  aE ( X )  b
and Var (Y )  a 2Var ( X ) ?