Math Answers

1.Solve the differential equation (2𝐷² + 5𝐷 + 2)𝑦 = 𝑒^{-1/ 2 x}

2. Solve the differential equation (𝐷3 − 3𝐷2 + 4𝐷 − 2)𝑦 = 𝑐𝑜𝑠𝗑.

Trace the following curves (x^2+y^2)x=2x^2+y^2

Use a Venn diagram to illustrate the subset of even integers in the set of all positive integers not exceeding 15.

Which is the upper 10%of the normal curve

let a and b be sets. show that (a∩b)⊆a

Dan works in an insurance company. Last January, he was able to insure 2 persons. Last February, he was able to insure 3 persons. Last March, he was able to insure 5 persons. Assume that samples of size 2 are randomly selected with replacement from this population of three values. a. List down the 9 different possible samples. b. Find the mean of each sample. c. Find the mean of the sampling distribution of means. d. Identify the probability of each sample. e. Find the population mean. f. Compare the population mean with the mean of the sampling distribution of means.

Colombo City typically has rained on about 16% of days in November.

a. What is the probability that it will rain on about 16% of days in November?

b. What is the mean number of days with rain in November?

c. What is the variance and standard deviation of the number of days with rain

in November?

Susan and Thomas play a game using two 10p coins. The coins are tossed and

Susan records her score using the random variable S and Thomas records his

score using the random variable T. After a large number of tosses they compare

their scores.

Comment on any likely differences and similarities.

Two fair cubical dice are thrown: one is red and one is blue. The random variable

M represents the score on the red die minus the score on the blue die.

a. Find the distribution of M.

b. Write down E(M).

c. Find Var (M)

Differentiate between ‘discrete’ and ‘continuous’ random variables with

appropriate examples.