robability Distributions
OR
Theoretical Distributions
Probability Distribution
x x
probability distribution of probability distribution of
discrete variable is known continuous variable is
a a
as Discrete probability distribution known as
continuous prob Distribution
V
when a variable is said to be variable is said to be
when a
a discrete variable a continuous variable
interval if nerva f
within a
given within a
given i
a variable can assume a variable can assume
It is infinite unlimited values It is
finite limited values
Discrete variable said to be a continuous
said to be a
variable
V x
Discrete probability distributions continuousprobability distributio
Binomial's Distribution Normal Distribution
Poisson's Distribution chi square E
Distribution
Multinomial's Distribution for student's Distribution
Geometric Distribution F Distribution
Rectangular Distribution
BP MGR N Chi t F
CA Vinod Reddy | Maths Regular Notes
, Binomial's Distribution
prob se as per
p
Binomial's theoremapproach Ca g
where n of independent
Number finite trials
D Number of successes in n trials
h se number of failures in n trials
in trial
probability of
success a
p single
probability of failure
in single trial
a
g
p 9 1 00 100
3 coins are tossed what is probability of getting
2 tails
classical homie
approach approach
All possible exactly likely n 3 p t 4 1 2 2
outcomes
prob 2 2
HH H HHT H TH HTT
se
TTT T TH TH T TH H ng pH gh 2
2
outcomes in favour 3g 1 t
T TH THT HTT 3g t E
nt 3 X X
t
probability
II.IE
NO of all possibleequal
3
8
0 3750
438 0.3750
37.501
37.507
CA Vinod Reddy | Maths Regular Notes
, S coins are tossed what is probability of
3 or 4 or s heads
getting
classical Binomial's
a
no of all possible etually likely n s
pet 9 2 2 3,4 s
outcomes 32 25
outcomes in favour prob 233
p x 3 Pfe 4 poets
HH HTT HH THT HHT TH
HH HHT HH H TH HHT HH Sgt Pt sq 7ft t
AHHHH HT HHT HTHTH S's E SCID
HTTHH
TH TH H
HTHHH TH HHT
TH H TH TH H HH
47 Sgt scat Sg
TTHHH 32 lots 1
I
501
soobability E 12
soy
2 dice are rolled what is probability of
s points on atleast one dice
getting
classical Binomials
of all possible dally f
No
likely outcomes
36 n 2 p 4
3 2 1,2
outcomes in favour prob 2 1
2
1,5 2,5 3,5 4,57 5,1 pfoe D pre
S2 5,37 5,47 5,5 5,6 1 Pfe o
6,5
I
2841 8
probability 30.555551 1 1 1
8 1
28
11
36 30.555551
CA Vinod Reddy | Maths Regular Notes
, 3 dice are rolled what is probability of getting
4 points on 2 dice
classical Binomial
outcomes infavour
2 2
414,1 4 9,27 9,9 3 9,4 s h 3 pet 9
8
44,6 4,447,44 2,4 413,4 Pfe 2
4,54 416,4 1 4,4 2,414 3g f f
314,4 5,441 6,4 4 1
No of all possible equally 3
3 34 8 2
6 216
likely out ones 6.9444
probability
6.944444
12 coins are tossed what is probability of
getting
i s heads
12cg Pt If 19.3359375
ii to tails 12g f off 49 1.611328125
Iii to or more heads Pfe 107 Pfe Il Ppe 12
I 129 E E 129 E E
12
11 t
t 1290 129 1292
66 12 1 79 1 92871
4096 40 96
CA Vinod Reddy | Maths Regular Notes
OR
Theoretical Distributions
Probability Distribution
x x
probability distribution of probability distribution of
discrete variable is known continuous variable is
a a
as Discrete probability distribution known as
continuous prob Distribution
V
when a variable is said to be variable is said to be
when a
a discrete variable a continuous variable
interval if nerva f
within a
given within a
given i
a variable can assume a variable can assume
It is infinite unlimited values It is
finite limited values
Discrete variable said to be a continuous
said to be a
variable
V x
Discrete probability distributions continuousprobability distributio
Binomial's Distribution Normal Distribution
Poisson's Distribution chi square E
Distribution
Multinomial's Distribution for student's Distribution
Geometric Distribution F Distribution
Rectangular Distribution
BP MGR N Chi t F
CA Vinod Reddy | Maths Regular Notes
, Binomial's Distribution
prob se as per
p
Binomial's theoremapproach Ca g
where n of independent
Number finite trials
D Number of successes in n trials
h se number of failures in n trials
in trial
probability of
success a
p single
probability of failure
in single trial
a
g
p 9 1 00 100
3 coins are tossed what is probability of getting
2 tails
classical homie
approach approach
All possible exactly likely n 3 p t 4 1 2 2
outcomes
prob 2 2
HH H HHT H TH HTT
se
TTT T TH TH T TH H ng pH gh 2
2
outcomes in favour 3g 1 t
T TH THT HTT 3g t E
nt 3 X X
t
probability
II.IE
NO of all possibleequal
3
8
0 3750
438 0.3750
37.501
37.507
CA Vinod Reddy | Maths Regular Notes
, S coins are tossed what is probability of
3 or 4 or s heads
getting
classical Binomial's
a
no of all possible etually likely n s
pet 9 2 2 3,4 s
outcomes 32 25
outcomes in favour prob 233
p x 3 Pfe 4 poets
HH HTT HH THT HHT TH
HH HHT HH H TH HHT HH Sgt Pt sq 7ft t
AHHHH HT HHT HTHTH S's E SCID
HTTHH
TH TH H
HTHHH TH HHT
TH H TH TH H HH
47 Sgt scat Sg
TTHHH 32 lots 1
I
501
soobability E 12
soy
2 dice are rolled what is probability of
s points on atleast one dice
getting
classical Binomials
of all possible dally f
No
likely outcomes
36 n 2 p 4
3 2 1,2
outcomes in favour prob 2 1
2
1,5 2,5 3,5 4,57 5,1 pfoe D pre
S2 5,37 5,47 5,5 5,6 1 Pfe o
6,5
I
2841 8
probability 30.555551 1 1 1
8 1
28
11
36 30.555551
CA Vinod Reddy | Maths Regular Notes
, 3 dice are rolled what is probability of getting
4 points on 2 dice
classical Binomial
outcomes infavour
2 2
414,1 4 9,27 9,9 3 9,4 s h 3 pet 9
8
44,6 4,447,44 2,4 413,4 Pfe 2
4,54 416,4 1 4,4 2,414 3g f f
314,4 5,441 6,4 4 1
No of all possible equally 3
3 34 8 2
6 216
likely out ones 6.9444
probability
6.944444
12 coins are tossed what is probability of
getting
i s heads
12cg Pt If 19.3359375
ii to tails 12g f off 49 1.611328125
Iii to or more heads Pfe 107 Pfe Il Ppe 12
I 129 E E 129 E E
12
11 t
t 1290 129 1292
66 12 1 79 1 92871
4096 40 96
CA Vinod Reddy | Maths Regular Notes
