MCA DCA7101 PROBABILITY AND STATISTICS

Description

PROGRAM MCA

SEMESTER III

COURSE CODE & NAME DCA7101 – PROBABILITY AND STATISTICS

SET-I

 

1. Bag I contain 3 red and 4 black balls and Bag II contain 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red. Find the probability that the transferred ball is black.

Solution: Step -1: Consider all possible events for transferring balls.

Given that,

Bag I contains 3 red and 4 black balls.

Bag II contains 4 red and 5 black balls.

Let E1, E2, E3, E, be events such that,

E1: Both transferred balls from Bag I to Bag II are red.

E2:

 

Its Half solved only

Buy Complete from our online store

 

https://smuassignment.in/online-store/

 

MUJ Fully solved assignment available for session SEPT  2023.

 

Lowest price guarantee with quality.

Charges INR 198 only per assignment. For more information you can get via mail or Whats app also

Mail id is aapkieducation@gmail.com

 

Our website www.smuassignment.in

After mail, we will reply you instant or maximum

1 hour.

Otherwise you can also contact on our

whatsapp no 8791490301.

 

2. A random variable has the following probability distribution

X	0	1	2	3	4	5	6	7
P(X=x)	0	a	2a	2a	3a	a^2	2a^2	7a^2 + a

 

Find

(i) the value of ‘a’

(ii) P [1.5<X<4.5/ X>2]

(iii) E(X)

(i)

Solution: Since it is a probability distribution, so, sum of all probabilities must be 1

 

 

3. The daily earning of a vendor for a period of 43 days are given below

Daily earning (Rs.)	118- 126	127- 135	136- 144	145- 153	154- 162	163- 171	172- 180
No. of days	3	8	9	12	5	4	2

 

Calculate Standard Deviation and coefficient of variation.

Solution:

 

Daily earnings	f	x	fx	(x-x̄)	F(x- x̄)	f(x- x̄)2
118-126	3	122	366	-23.86	-71.58	1707.90
127-135	8	131	1048	-14.86	-118.88	1766.56
136-144	9	140	1260	-5.86	-52.74	309.06
145-153	12	149	1788	3.14	37.68	118.32
154-162	5	158	790	12.14	60.7	736.90
163-171	4	167	668	21.14	84.56	1787.60
172-180	2	176	352	30.14	60.28	1816.84
	Fx=43		∑fx=6272			∑f(x- x̄)2=8243.18

 

Mean x̄=

 

SET-II

 

4. Suppose that a manufactured product has 2 defects per unit of product inspected. Using Poisson’s distribution, calculate the probabilities of finding a product without any defect, 3 defects, and 4 defects. (Given)

Solution:

Given:

A manufactured product has 2 defects per unit of product inspected

To find:

The probabilities of finding a product with

• out any defect

 

 

5. Compute the regression equation of Y on X and regression equation of X on Y on the basis of the following information

	X	Y
Mean	40	45
Standard Deviation	10	9

 

The correlation coefficient between X and Y is 0.50. Also estimate the value of Y for X = 48, using the appropriate regression equation.

Answer:

 

Given that,

The line of regression fo

 

 

 

6. The following data relate to the prices and quantities of 4 commodities in the years 1982 and 1983. Construct the following index numbers of price for the year 1983 by using 1982 as base year.

(i) Laspeyre’s Index

(ii) Paasche’s Index

(iii) Fisher’s Index

 

Commodit Y	1982			1983
	Price	Quantity		Price		Quantity
A	5		100	6	150
B	4		80	5	100
C	2.5		60	5	72
D	12		30	9	33

 

Solution:

Commodit Y	1982		1983		P1q0	P0q0	P1q1	P0q1
	Price(P0)	Quantity(Q0)	Price(P1)	Quantity(Q1)
A	5	100	6	150	600	500	900	750
B	4	80	5	100	400	320	500	400
C	2.5	60	5	72	300	150	360	180
D	12	30	9	33	270	360	297	396
Total					1570	1330	2057	1726