Math Answers

A production facility contains two machines that are used to rework items that are initially defective. Let 𝑋 be the number of hours that the first machine is in use and let 𝑌 be the number of hours that the second machine is in use, on a randomly chosen day. Assume that 𝑋 and 𝑌 have a joint probability density function given by 𝑓(𝑥) = { 3 2 (𝑥 2 + 𝑦 2 ) 0 < 𝑥 < 1 𝑎𝑛𝑑 0 < 𝑦 < 1 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒. a. What is the probability that both machines are in operation for less than half an hour?

Mr. X is known to hit the target in 4 out of 5 shots, where as Mr. Y is known to hit the target in 3 out of 5 shots. Find the probability that both will hit the Target

Draw a simple, undirected graph yourself, the vertices are connected with each other including 8 vertices and 14 edges. Find the shortest path from two arbitrary vertices:​

a) The weight of each edge is 1.​

b) Self-weighting for edges

State TRUE or FALSE justifying your answer with proper reason.

a. 2𝑛^2 + 1 = 𝑂(𝑛^2 )

b. 𝑛^2 (1 + √𝑛) = 𝑂(𝑛^2 )

c. 𝑛^2 (1 + √𝑛) = 𝑂(𝑛^2 log 𝑛)

d. 3𝑛^2 + √𝑛 = 𝑂(𝑛 + 𝑛√𝑛 + √𝑛)

e. √𝑛 log 𝑛 = 𝑂(𝑛)

find inverse laplace transorm : se^-2s/(s^2 + pi^2)

The following table shows the income distribution of 600 families. Find the minimum income

of the riches 30% families. Also the limits of income of middle 50% of families, to the nearest

rupees.

Income Below

75

75-

150

150-

225

225-

300

300-

375

375-

400

400 &

above

No. of

families

69 137 225 46 88 25 10

Ans.: the richest 30 % families earns Rs. 222 and above per week , the middle 50% families

weekly income lies between 120 and 256.

The raw data has been organised in the frequency table below.

games frequency

6 2

7 5

8 n

9 4

10 4

11 2

12 2

13 2

(a) Write down the value of n.

(b) Calculate the mean number of games played per set.

(c) What percentage of the sets had more than 10 games?

(d) What is the modal number of games?

A spring is such that a 16 lb weight stretches it by 1.5 in. The weight is pulled down to a point

4 in below the equilibrium point and given an initial downward velocity of 4 ft/sec. An impressed

force of F(t) = 2 cos 74t is acting on the spring. Describe the motion.

Calculate the quartiles, (i,e., Q1 and Q3,), deciles D3 and D7, Percentiles P10, P23 and P92 for the

following data. Also find the Quartile Range and Quartile Deviation.

Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

No. of Students 8 7 5 12 28 22 8 10

A. Solve the following problems:

1. On the assumption that variables are continuous, compute for the median of the following data:

a. 1, 4, 5, 9, 11

b. 4, 8, 16, 27, 52

c. 7, 26, 31, 36, 46, 65

2. Calculate the range for the following sets of measurements:

a. 3, 6, 7, 10, 2

b. 11, 27, 32, 45, 54

3. Calculate the variance and standard deviation of the following: 13, 18, 21, 19, 16, 15.