MCA DCA7101 PROBABILITY AND STATISTICS

Description

SET 1

 

1. Suppose a person throws a die. If he gets a 5 or 6, he tosses a coin three times and notes the number of heads. If he gets 1, 2, 3 or 4, tosses a coin once and notes whether a head or tail is obtained. If he obtained exactly one head; what is the probability that he threw 5 or 6 with the die.

 

Ans 1.

The solution to this problem involves Bayes’ theorem, which states that P(A|B) = P(B|A) * P(A) / P(B), where P(A|B) is the probability of event A given event B is true, P(B|A) is the probability of event B given event A is true, P(A) is the probability of event A, and P(B) is the probability of event B.

We want to find the probability that the die

 

Its Half solved only

Buy Complete from our online store

 

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

 

MUJ Fully solved assignment available for session March  2023.

 

Lowest price guarantee with quality.

Charges INR 200 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

 

 

Find (i) the value of ‘’

 

 

(iii)

 

(i)

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

Since, “a” is a probability, so, it cannot be negative

A = 0.1

(ii) [1.5<x<4.5/x>2]

 

When 1.5<x<4.5 =2a+3a

=5a

=5(1/10)

=1/2 or 0.5

 

When x>2 =P(X=3)+ P(X=4)+ P(X=5)+ P(X=6)+ P(X=7)

= 2a+3a+ a²+2a²+7a²

=5a+10a²

=5(1/10)+10(1/10)

 

 

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

 

           

 

 

SET-II

 

 

 

4. The probability that a bomb dropped from a plane will strike the target is 1/5. If 6 bombs are dropped, find the probability that-

 

1. Exactly two will strike the target.
2. Atleast two will strike the target.

 

Ans 4.

To answer this question, we’ll need to use the binomial probability formula, which is as follows:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

where: P(X=k) is the probability of k successes in n trials, C(n, k) is the number of combinations of n items taken k at a time (also known as “n choose k”), p is the probability of success on a given trial, and (1-p

 

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.

 

Ans 5.

 

Given that,

 

 

 

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.

 

1. Laspeyre’s Index
2. Paasche’s Index

iii. Fisher’s Index

Commodity	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

 

Ans 6.

 

Solution:

 

Commodit Y	1982		1983		P1q0	P0q0	P1q1	P0q1
	Price(P0)	Quantity(Q0)	Price(P1)	Quantity(Q1)