ISTANBUL
NISANTASI
University
EXAM QUESTION AND ANSWER SHEET
Question 11. The CDF of random variable x is:
P[(-1)/(2)]<=x<=[(3)/(7)]Mr(5)/(16)11isxYPOFfr(y)f_(r)(y)={((1)/(2)y,0<=y<1),(0 otherwise ):}xf_(x)(x)={(cx,0<=x<=2),(0 otherwise ):}PDFc_(. )xYFDF{(:f_(x,y)(x,y)={((1)/(15),0<=x<=5,0<=y<=3):}):}
0 otherwise /PI 2<=x<3,1<=Y<31(1)/(15)u(x)=(ddelta (x))/(dx)delta (x)=(d^(2)u(x))/(dx^(2))delta (x)=(du(x))/(dx)(1)/(15)delta (x)=u(x)/(x)delta (x)=(d^(2)u(x))/(dx^(2))f,(y)={[y,0]}
(c)
(d)
f_(r)(y)={((1)/(2)y,0<=y<1),(0 otherwise ):}
Question 13. The random variable x has probability gravity function
f_(x)(x)={(cx,0<=x<=2),(0 otherwise ):}
Use the PDF to find the constant c_(. )
af_(V)(y)={[(1)/(2)y,0]}
(a)
(b)
f,(y)={[y,0]}
(c)
(d)
f_(r)(y)={((1)/(2)y,0<=y<1),(0 otherwise ):}
Question 13. The random variable x has probability gravity function
f_(x)(x)={(cx,0<=x<=2),(0 otherwise ):}
Use the PDF to find the constant c_(. )
a0
What are the marginal PDF fr(y) ?
f_(V)(y)={[(1)/(2)y,0]}
(a)
(b)
f,(y)={[y,0]}
(c)
(d)
f_(r)(y)={((1)/(2)y,0<=y<1),(0 otherwise ):}
Question 13. The random variable x has probability gravity function
f_(x)(x)={(cx,0<=x<=2),(0 otherwise ):}
Use the PDF to find the constant c_(. )
af_(xy)(x,y)=
0
0
What are the marginal PDF fr(y) ?
f_(V)(y)={[(1)/(2)y,0]}
(a)
(b)
f,(y)={[y,0]}
(c)
(d)
f_(r)(y)={((1)/(2)y,0<=y<1),(0 otherwise ):}
Question 13. The random variable x has probability gravity function
f_(x)(x)={(cx,0<=x<=2),(0 otherwise ):}
Use the PDF to find the constant c_(. )
af,(x)={[(1)/(4),-2]}
Find P[(-1)/(2)]<=x<=[(3)/(7)] ?
(a) 1
(b) Mr
c
Grismons
Find the MGF Fir _(k)(s)
P_(n)(k)=int_0^(9*2) ,k=0,1,2,3_( others )
a) phi ^(2)(t)=6*2(t+e^(2)+e^(3n)+e^(3n))
b) Fx(s)=1+e^(2)+e^(2)+a^(3)
e) Phi _(k)(s)=0*2(e^(2)+r^(3x)+e^(3n))
F(x)-0*2(x+x+x^(x)+x^(3))
Question 2. x is a uniform random variable with parameters of -3 and 3. What is the Var DCI?
a) 3
b) 9
Question 3, x is an exponential random variable with, What is the variance of xC?
a) (1)/(16)
b) 1:4
e) 3.5
d) 16
Question 4. The probability density function of random variable Y is
E[Y|Y|]<=[6]xYY=ax+bVar[Y]=a^(2)Var[x]+bVar[Y]=a^(2)Var[x]Var[Y]=aVar[x]Var[Y]=Var[x]x(3)/(5)f_(x)(x)={[3x^(2),-1]}
What is the Var[X]?
(a) 3
(b)( 3)/(5)
cf_(r)(y)={[(1)/(10),0]}
Find the E[Y|Y|]<=[6]
(a) 2.5
(b) 2
c
Question 1, Random arihe Khs PMF
SNOLLSED
0.17 others
Find the MGFs =0.21+ s=02++
s-0.z1+
Question 2. X is a uniform random
s the VarX
Question 3. X is an exponential random variable 1/16 c3.5 16 Question 4. The probability density function of random variable Y is 1/100<y<10 others Find the E[Y[Y6] a2.5 b)2 c3 3.5 Question 5. There are two random variables X and Y which Y-aX+b which of the following is correct bVar[Y]=aVar[X] aVar[Y]=aVar[X]+b dVar[Y]=Var[X] cVar[Y]=aVar[X] Question 6. The probability density function of random variable X is -1<x<1 others What is the Var[X]
a3 ( 0
d) 6/5
Document No: BOFR26/Release Date: 11.08.2022 Release Date: 16.11.20
