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MSO

2}la:

probability

and

Statistics

2015-2016_II

Semester

Assignment_XI

A.

fllustrative

Discussion

problems

1.

Suppose

that

the

lifetime

of

electric

bulbs

exponential

distribution

with

mean

of

50

random,

rnanufactured

by

a

manufacturer

follows

hours.

Eight

such

buibs

are

chosen

at

than

40

between

lifetime

lifetime

lifetime

(a)

Find

the

probability

that,

among

eight

chosen

bulbs,

2

w'l

iast

ress

hours,

3

will

last

anywhere

between

40

and

60

hours,

2

w'l

last

anywhere

60

and

80

hours

and

1

will

last

for

more

than

g0

hours;

(b)

Find

the

expected

number

of

burbs

in

the

rot

of

chosen

g

burbs

with

between

60

and

g0 hours;

(c)

Find

the

expected

number

of

bulbs

in

the

rot

of

B

chosen

burbs

with

between

60

and

g0

hours,

given

that

the

number

of

burbs

in

the

lot

with

anywhere

between

40

and

60

hours

is

2.

2'

suppose

that

x

-

(xr,

Xz,Xs,xs)

-

Murt(30,

0r,gz,0s,g+).

Find

the

conditional

probabilitv

mass

function

of

(Xt,Xz,Xz,Xq)

given

that

Dl=,

Xn:

2g.

'

:;t:ffi;n"

a

-

A&(0,0,

1,

1,0).

Find

c1

such

that

p(-c1

(

Xr

(

C7,

_ct

{

Xz {

4'

Let

X:

(Xr,Xr)'

-

Nz(t"r,l,tz,o?,o2,

p)

'i

:

I,2,3,4,

aps

I

azae),

let

y

:

arXt

and,

for

constants

ar,a2,a3

and

as

(at

I

0,

I

a2X2

and'Z

:

asXt

I

aaX2.

(a)

Find

the

joint

p.d.f.

of

(y,

Z);

(b)

Find

the

marginai

p.d.f.s.

of

y

and

5. (u)

Let

(X,

Y)'

-

Nz(5,

8,

16,

9,

0.6).

Find

p({b

< },

< 11ii{X

:

2}),

p({4

)

\

t-r..-

r,

rv

tdt

\]t,

}:.^

,

\

\1

t'.

'-si l_D/

r_s;

\b.

lv.

b

[c*

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h*=:

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=\

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